Cross-National Commonalities and Differences in the Intended Curriculum in Primary School Reading and Mathematics
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Cross-National Commonalities and Differences in the Intended Curriculum in Primary School Reading and Mathematics

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The overarching purpose of the present study, commissioned by UNESCO‘s Institute for Statistics, is to compile, analyze and describe commonalities and differences in the intended primary curriculum ...

The overarching purpose of the present study, commissioned by UNESCO‘s Institute for Statistics, is to compile, analyze and describe commonalities and differences in the intended primary curriculum in reading and mathematics across a diverse set of developing countries.

The specific activities to be carried out include the following: Compile materials on the intended reading and mathematics curriculum in the final grades of primary education from a significant number of developing countries (around 25-30), and ensure adequate coverage by region and language (i.e., at least in English, Arabic, Spanish and French); Develop and validate a coding scheme to systematically record, retrieve and compare the intended reading and mathematics curriculum in different primary education systems; Discuss an interim set of products emerging from the aforementioned project activities, including the coding scheme, with the IWG through electronic means and IWG meetings; Complete all compilation activities and cross-national analyses of the intended reading and mathematics curriculum and submit a draft report for review by the IWG and UNESCO colleagues. Submit a final report with the study‘s main findings.

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    Cross-National Commonalities and Differences in the Intended Curriculum in Primary School Reading and Mathematics Cross-National Commonalities and Differences in the Intended Curriculum in Primary School Reading and Mathematics Document Transcript

    • International Working Group on Assessing and Improving Quality LearningCross-national Commonalities and Differences in theIntended Curriculum in Primary School Reading andMathematics1 Date: February 7, 20111 Prepared by Aaron Benavot (Institutional affiliation: Department of Educational Administration and Policy Studies and the Institute for Global Education Policy Studies, University at Albany-State University of New York) for the UNESCO Institute for Statistics, Montreal, Canada. The author wishes to thank the following colleagues and students for their expertise and efforts in support of this project: Dr. Gilbert Valverde, Dr. Samira Alayan, Dr. Lilia Verónica Toranzos, Dr. Yi-Jung Wu, Treisy Romero, Marcellus Taylor, Gloria Zambrano, Polinda Keo, Fadi Kanaan, Zakhar Berkovich, Laurence Padjip, Julliet Ochienghs, Laura Manley, Dr. Prachayani Praphamontripong, Yaser Robles, Hue Do, Perveen Faisal, Muhammad Mubeen, Newshaw Bahreyni, Rostati Rostati, Chinthaka Jayawardena, Faisal Yaqoob, Zafar Aminov and Dhanushki Samaranayake. 1
    • Table of ContentsI. Background ………………………………………………………………………………4II. The ‗Learning Counts‘ initiative……………………………………………………….…5III. The commissioned study……………………………………………………………….…6IV. Past research of the intended reading and mathematics curriculum ………….…7V. Compiling, coding and comparing intended reading and mathematics curricula………...8 1. Construction of the international archive of curricular documents……...………..………8 2. How representative and diverse are the curriculum materials in the international archive?…………………………………………………………………………………..12 3. Developing a coding scheme to compare curricular documents…………...……………16 4. Language issues…………………………………………………………….………….17 5. Document profiles resulting from the coding process……………………….………...18 6. Quality assurance in coding procedures……………………………………….………19 7. Creating ‗master tables‘ of profiles and setting benchmarks for comparison…………20VI. Results………………………………………………………………………………...…21 1. Commonalities in the intended curricula of developing countries………………….…22 2. Alignment between official curricular intentions and textbooks………………...……25 3. Establishing challenging standards in mathematics curricula…………………...….…28VII. Discussion and concluding remarks………………………………………………….….30VIII. Suggestions for future activities…………………………………………………..….….34IX. References……………………………………………………………………………….36Tables 2 thru 9……….……………………………………………………………….………….40List of FiguresFigure 1: Percentages of primary school enrolments in each region that are represented by curriculum materials in the international archiveFigure 2: Weighted regional averages of GNP per capita (2007) for countries included in the archive as compared to the average of all developing countries in the regionFigure 3: The number of official curricular statements and guidelines in the international archive, by languageFigure 4: The number of textbooks and exercises in the international archive, by languageFigure 5: Number of countries in each of the eight ‗master tables‘Figure 6: Alignment between official curriculum and mathematics textbooks, grades 5 and 6Figure 7: Alignment between official curriculum and reading textbooks, grades 5 and 6Figure 8: The emphasis placed on cognitively challenging performance standards in mathematics guidelines, by country and grade levelFigure 9: Figure 9: The emphasis place on cognitively challenging performance standards in mathematics textbooks, by country and grade level 2
    • List of TablesTable 1: Overview of curricular materials obtained for each country/education system, by document type and subjectTable 2: Common contents and performance expectations in mathematics in grade 6, based on an analysis of textbooksTable 3: Common contents and performance expectations in mathematics in grades 5 and 6, based on an analysis of textbooksTable 4: Common contents and performance expectations in mathematics in grade 6, based on an analysis of curriculum statements and guidelinesTable 5: Common contents and performance expectations in mathematics in grades 5 and 6, based on an analysis of curriculum statements and guidelinesTable 6: Common contents and performance expectations in reading in grade 6, based on an analysis of textbooksTable 7: Common contents and performance expectations in reading in grades 5 and 6, based on an analysis of textbooksTable 8: Common contents and performance expectations in reading in grade 6, based on an analysis of curriculum statements and guidelinesTable 9: Common contents and performance expectations in reading in grades 5 and 6, based on an analysis of curriculum statements and guidelines 3
    • I. BackgroundCountries and international organizations have long sought to universalize access to primaryeducation, with considerable success. However, it was not until the Jomtien Declaration (1990),and later the Dakar Framework For Action (2000), that quality education came to be recognizedas a crucial component of the Education for All (EFA) agenda. At Dakar national governmentsand international stakeholders committed themselves to ensuring that ‗by 2015 allchildren…have access to, and complete, free and compulsory primary education of good quality’(EFA goal 2). They also pledged to improve ‘all aspects of the quality of education…so thatrecognized and measurable learning outcomes are achieved by all, especially in literacy,numeracy and essential life skills‘ (EFA goal 6).The Expanded Commentary on the Dakar Framework of Action (2000:15-17) went a stepfurther. It stressed that ―quality is at the heart of education, and what takes place in classroomsand other learning environments is fundamentally important to the future well-being of children,young people and adults.‖ Access to quality basic education is a fundamental right for all. ―Noone should be denied the opportunity to complete good quality primary education because it isunaffordable….[I]mproving and sustaining the quality of basic education is equally important [touniversalizing primary education] in ensuring effective learning outcomes….‖ Quality educationshould ―satisfy basic learning needs, and enrich the lives of learners.…‖ The necessaryconditions for quality education were also laid out: well-trained teachers and active learningtechniques; adequate facilities and instructional materials; clearly defined, well-taught andaccurately assessed curricular knowledge and skills; and a healthy, safe, gender-sensitiveenvironment that makes full use of local language proficiencies.Interest in all aspects of quality in education has certainly blossomed since Dakar. Especiallyamong governments, donors, international agencies and NGOs, policy discussions of qualityissues have steadily increased. Of note, for example: Several international, ministerial-level meetings have focused extensively on quality education (e.g., International Conference on Education, Geneva, 2004; Intergovernmental Meeting of the Regional Project in Education for Latin America and the Caribbean, Buenos Aires, 2007); An influential World Bank report recommended that countries and development partners emphasize learning outcomes as well as school access to improve the economic and social gains from current investment in primary education (World Bank Independent Evaluation Group, 2006); The EFA Fast Track Initiative established a Quality of Learning Outcomes Task Team, which eventually recommended that quality measures such as the monitoring of learning outcomes be incorporated as additional criteria in the endorsement of EFA-FTI country plans (FTI technical meetings in Moscow 2006, Cairo 2006 and Bonn 2007); Several UNESCO initiatives focused on quality education: for example, teacher training and development in sub-Saharan Africa (TISSA) as well as learning processes (‗Enhanced learning: From access to success‘) and learning assessments in Africa (SACMEQ) and Latin 4
    • America (UNESCO, 2007a); In 2006 many governmental and non-governmental organizations participated in a Global Action Week, which highlighted quality issues such as teacher supply and pre- and in-service teacher training; Recent EFA Global Monitoring Reports have compiled considerable evidence of inequalities in quality education (both between and within countries) and growing participation in international, regional and national assessments of student learning (UNESCO 2007b; UNESCO 2008).To be sure, the increased attention to the challenges of improving quality education ininternational policy fora and reports mainly illustrates how these themes are incorporated inofficial statements, intentions and plans. Such ‗actions‘, while underscoring stakeholdercommitment to a core element of the EFA framework, tell us little about real changes in theprovision of quality education and improved learning outcomes. Indeed, comparativeassessments of student achievement consistently report large cross-national differences inlearning outcomes between developed and developing countries as well as low absolute learninglevels across many, if not most, developing countries (UNESCO 2008; UNESCO 2009).Learning outcomes are especially unequal within countries. They tend to fall along well-knownfault lines: according to poverty, rural-urban residence, region, parental education, gender anddisability as well as among different indigenous, ethnic, immigrant and language groups.2 Overtime, these lingering achievement disparities tend to exacerbate socio-economic inequalities,reinforce inter-generational cycles of poverty, and perpetuate the marginalization ofdisadvantaged groups. Thus, equalizing the actual provision of quality education and improvinglearning outcomes—that is, moving beyond official declarations and policy intent--constitutes acritical global challenge in education, especially for countries in the developing world. II. The ‘Learning Counts’ initiativeTo support country efforts to improve quality education for all, and within its broader EFAmandate, UNESCO convened a special seminar entitled ‗Learning counts: An internationalseminar on assessing and improving quality education for all‘ in Paris on 28-30 October 2008,which brought together international experts in the areas of quality education and assessment.The seminar enabled participants to exchange a multiplicity of ideas and experiences on howquality learning is conceptualized, implemented and measured in different contexts, as well asthe particular learning challenges facing developing countries and educationally disadvantagedpopulations.The Learning Counts seminar led to the establishment of the International Working Group onAssessing and Improving Quality Learning (IWG), which was charged with: A. Exploring and discussing points of convergence among multiple approaches seeking to conceptualize, assess and improve quality education at the level of the learner, the school2 Evidence of within-country inequalities is reported in Casassus et al. (2002), UNESCO-OREALC (2007), Martin et al (2004), Mullis et al. (2004), OECD (2004), OECD (2007), Torney-Purta et al. (2001), Mullis et al. (2007) and Ma (2008). 5
    • and the system. Specifically, the IWG was tasked with seeking consensus on a set of common core indicators of quality education in primary education for a broad range of countries and providing recommendations to be considered by relevant national and international stakeholders. B. Addressing the broader dimensions of quality by focusing on indicators of the enabling conditions for learning, including the acquisition of knowledge, values and skills in the cognitive and affective domains, as well as actual teacher practices and classroom effectiveness.During the first meeting of the International Working Group (5-6 March 2009) participantsagreed that participation in quality primary education implies, among other things, theachievement of core learning proficiencies in literacy, numeracy and essential life skills by theend of the primary cycle. They noted that the structure of primary education varies acrosscountries--and sometimes within countries--and there is a need to draw upon the InternationalStandard Classification of Education (ISCED) to define the upper grades of the primaryeducation.They also underscored the importance of examining intended curricular structures, guidelinesand contents to ascertain the extent to which countries‘ goals or standards in reading andnumeracy, at the end of the primary cycle, or at the end of the segment of the cycle wherereading and numeracy are explicitly taught, can underpin a statement of minimum desiredcompetencies. In principle, they thought that country initiatives in conjunction with thisstatement could be used to drive improvements in learning assessments and outcomes, and in theprovision of quality education.The IWG agreed that UNESCO should commission, as part of its background activities, acomprehensive review of the intended contents of reading and mathematics curricula in the lattergrades of primary education in diverse developing countries. Such a study would attempt toidentify a core set of common contents and performance expectations in reading andmathematics, which could then serve as the basis for recommendations regarding the types ofdomains to measure minimal and/or desirable learning outcomes to be achieved by students inthese subjects by the end of primary education. Assessing such core learning outcomes couldplay an important supplemental role in monitoring the overall performance and effectiveness ofnational primary school systems. The proposed study might also indicate which developingcountries have established a more or less ‗demanding‘ or cognitively challenging curriculum inliteracy and numeracy. III. The commissioned studyThe overarching purpose of the present study, commissioned by UNESCO‘s Institute forStatistics, is to compile, analyze and describe commonalities and differences in the intendedprimary curriculum in reading and mathematics across a diverse set of developing countries.3The specific activities to be carried out include the following:3 The category of ‘developing countries’ follows the UNESCO classification of countries from the following regions: Arab States; East Asia and the Pacific (excluding Japan, Australia and New Zealand); Latin America and the Caribbean (excluding Bermuda); South and West Asia; sub-Saharan Africa; as well as Cyprus, Israel, Mongolia and Turkey. 6
    • Compile materials on the intended reading and mathematics curriculum in the final grades of primary education from a significant number of developing countries (around 25-30), and ensure adequate coverage by region and language (i.e., at least in English, Arabic, Spanish and French); Develop and validate a coding scheme to systematically record, retrieve and compare the intended reading and mathematics curriculum in different primary education systems; Discuss an interim set of products emerging from the aforementioned project activities, including the coding scheme, with the IWG through electronic means and IWG meetings; Complete all compilation activities and cross-national analyses of the intended reading and mathematics curriculum and submit a draft report for review by the IWG and UNESCO colleagues. Submit a final report with the study‘s main findings. IV. Past research of the intended reading and mathematics curriculum4Previous cross-national studies of the official intended primary curriculum have analyzednational timetable data to describe broad curricular trends and patterns in some 80-100 countries(Meyer, Kamens and Benavot 1992; Benavot 2008). These studies report global and regionalvariation, over time and place, in the prevalence of, and the relative emphasis on, language andmathematics instruction (as well as other subject areas) in primary education, sometimes bygrade level. In a different vein, comparative research conducted during the initial TIMSSassessment identified core mathematics and science contents and performance expectationscommon to primary and secondary schooling in almost 50 mainly developed nations. Theidentification of these shared contents and performance standards emerged from a detailed page-by-page content analysis of nationally representative samples of curriculum guidelines andtextbooks (Schmidt et al. 1997; Valverde 2000; Valverde et al. 2002; Valverde and Schmidt2000).Other international and regional learning assessments have collected subject- and grade-specificinformation about intended curriculum of participating countries, usually in conjunction with thedevelopment of standardized test items. For example, recent TIMSS and PIRLS assessmentsexamined select information about mathematics, science and reading curricula for grade 4students in many high-income and some middle-income countries. Regional assessments havecompiled select curricular information about: grade 6 mathematics and reading curricula in 15 sub-Saharan African countries (SACMEQ); grades 2 and 5 mathematics and language curricula for about 20 sub-Saharan African countries (PASEC); and grades 3 and 6 mathematics and reading curricula for the 16 Latin American countries (LLECE and SERCE).4 While the official intended curriculum certainly structures what is actually taught in local schools and classrooms (the implemented curriculum), the gap between the intended and implemented curriculum can vary significantly within and across countries and even by subject area (see, for example, Resh and Benavot 2009). Many assume, based on limited comparative evidence, that the gap between the intended and implemented curriculum is considerably wider in the educational systems of the developing world. 7
    • With an eye towards building upon the knowledge base of these assessment exercises, severaldiscussions and exchanges were conducted with relevant colleagues. It became clear that, insome instances, official documents and textbooks had been compiled and utilized within thecontext of these assessments. However, for various reasons (e.g., grade levels examined, thedetail of coded contents), and given this study‘s particular focus, it was concluded that compiledmaterials from previous regional assessments would be of limited value in the effort to identifycommon core elements in literacy and numeracy education across diverse developing countries. V. Compiling, coding and comparing intended reading and mathematics curricula1. Construction of the international archive of curricular documentsThe project‘s first task was to build up an international collection of official, up-to-datecurricular documents related to the teaching of reading and mathematics in a diverse array ofdeveloping countries.5 Ideally, this meant obtaining two types of government sanctioneddocuments for each country: 1) Official documents outlining the intended curriculum in language/reading and mathematics in grades 4-6; or, alternatively, grade-specific programs of study (syllabi) or teacher guidelines, prepared by a curriculum development unit in the ministry (or official government authority), which describe the topics and performance standards in reading and mathematics for students in grades 4-6; 2) Officially sanctioned textbooks in reading/language and mathematics for grades 4-6; or, in the absent of officially mandated textbooks, the most widely used, commercially produced textbooks in each subject area.Beginning in August of 2009 the project team contacted international organizations (e.g.,UNESCO‘s International Bureau of Education, the G. Eckert Institute for International TextbookResearch), assessment and curriculum experts, national ministry officials, and academiccolleagues to determine if they possessed (or could obtain) the types of curriculum documentsnoted above either in a digital or hard-copy format. These contacts resulted in gaining access tomany curriculum materials. In subsequent months additional documents were obtained throughexchanges with international colleagues and by using informal networks of graduate students atthe University at Albany-SUNY.6 With the help of many people in many countries and5 In addition to the fact that competence in reading and mathematics is explicitly noted in the EFA goals, many argue, correctly, that student knowledge and skills in these core areas influence student progress in other curricular areas. Indeed, elements of reading and mathematics are often integrated in the teaching of other subject areas, as a mechanism of reinforcement. Furthermore in many primary schools, the same teacher is responsible for instruction in all subject areas, thereby making the reinforcement of core skills more likely.6 The project also gathered information about three potentially useful textbook collections: 1) the G. Eckert Institute for International Textbook Research in Braunschweig, Germany, which concentrates on analyzing social studies textbooks in history, geography and civics education; 2) a cross-national study of social science textbooks at Stanford University, which augmented materials initially identified at GEI (see Meyer, Bromley and Ramirez 2010); and 3) an older collection at the Institute of Education (IoE) at the University of London consisting of various textbooks from developing countries. In the first two collections, not surprisingly, there are almost no textbooks related to mathematics and language, since these subject areas have not been the focus of attention. Inquires to the IoE in London indicate that the Institute’s textbook collection is significantly out of date and fairly limited in terms of geographical coverage. 8
    • institutions, the project eventually assembled a surprisingly large compilation of curricularmaterials from around the globe. In October 2009 several experts and UAlbany graduate studentsbegan archiving the initial collection of textbooks and documents (digital ones were printed out)and finalized relevant coding schemes and procedures (see below).The compilation of curriculum documents and textbooks continued throughout the 2010 calendaryear. By December 2010 the newly established International Curriculum and Textbook Archive(ICATA) had amassed over 660 curricular guidelines, textbooks and other related documents,which represent different aspects of the intended contents of reading and mathematics for about60 developing countries or autonomous education systems.7 In most cases, the compileddocuments provide an incomplete picture of the intended reading and mathematics curriculum ingrades 4-6. (A future goal is to obtain supplemental materials to complete the curricular portraitof such countries). Nevertheless, to the best of our knowledge, the ICATA is the largest archiveof curricular materials pertaining to developing countries in the world.Archived documents were initially classified into six types: curriculum statements, guidelines,textbooks, exercise books, tests and articles.8 It was subsequently determined that almost alldocuments could be easily subsumed under two general categories: (1) textbooks and exercisebooks; and (2) official curriculum statements and guidelines. Documents in the former categoryare usually developed by curriculum specialists and subject experts (many of whom work inacademia or outside the educational system) and used extensively by teachers for instructionalpurposes. They define the intended knowledge domains and topics to be taught in the classroom,together with the performance standards that students are expected to achieve as a result ofclassroom instruction. They frequently constitute the basis for constructing test items for end-of-term or end-of-cycle learning assessments. Typical of the documents in the latter category is anational statement outlining the curricular policies and aims, as well as the intended curriculum(program of studies) in language and/or mathematics, for a specific primary grade. Documents inboth categories, particularly the latter one, often mention other educational policies andintentions—for example, statements of broad educational goals, teaching methods, pedagogicalphilosophies and expected non-cognitive learning outcomes. Given the present study‘sobjectives, it was decided to focus exclusively on the analysis of subject contents and cognitiveperformance expectations.7 For those interested in a detailed listing of the contents of the ICATA, go to http://www.albany.edu/eaps/international.shtml and look under ‘ICATA’. This listing delineates the type, title and language of the document with the date and place of publication, and notes the curricular subject and grade level(s) to which it refers. Almost all the documents in the ICATA refer to a single country. The one exception is the case of the Eastern Caribbean, in which an official document provides information on the curricular intentions of 5 small Caribbean states and 4 nearby territories, which share a common curriculum. Of the over 660 documents in the ICATA, over 580 have been identified as relevant to this study. The remaining documents have been placed aside since they are: 1) no longer current, 2) refer to developed countries, 3) relate to grades 1-3; and/or 4) deal with subject areas other than reading and mathematics.8 Curriculum: an official government statement detailing, among other things, the topics to be taught in particular subjects and grade level(s) and performance expectations or goals; Guideline: an official document detailing curriculum-related instructions to curriculum developers, textbooks writers and/or teachers; Textbook: a subject- and grade-specific text that details and structures classroom instruction and pupil learning; Exercise: a book, often accompanying a textbook, that includes specialized problems and exercises for students to complete so as to develop their skills and knowledge in a specific topic; Test: a written instrument used by teachers to evaluate student knowledge and skill performance; Article: a published report or study discussing or analyzing the intended curriculum in a country or region. 9
    • In total, about 580 curricular documents fell within the specific parameters of this study--that is,they refer to official reading or mathematics statements, guidelines or textbooks; pertain togrades 4, 5 or 6; and are used in the public primary schools of a developing country. Almostthree-quarters (74%) of these documents are either textbooks, or exercise books accompanyingtextbooks. About one-quarter (26%) constitutes official curriculum statements or guidelines.9The predominance of textbooks is not surprising since they are specifically designed to conveyconcrete school knowledge in a given subject at a particular grade level. Textbooks translateabstract curricular policies into concrete pedagogical activities that teachers and students enact inthe classroom. As such, they are suggestive of policy enactment, and have been characterized asthe ―potentially implemented‖ curriculum—a mediator between policy intention and policyimplementation (Valverde et al. 2002).By contrast, official curricular statements/guidelines tend to be more comprehensive documents,and often contain policy information for multiple subjects and grade levels. They provide anoverall rationale and blueprint of curricular policies to be implemented. They act as policydirectives that schools, principals and teachers are meant to put into practice. The morecomprehensive character of official curriculum statements can be seen in the country coveragereported in Table 1. While the archive includes a smaller number of such documents, theyprovide curricular information for 43 countries10; textbooks, though greater in number, provideinformation for about the same number of countries—from 39 in mathematics to 44 in reading.11Scholars and policy analysts often raise questions as to the extent to which the curricularcontents and expectations detailed in official statements and guidelines are in alignment withthose found in authorized textbooks. In the results section, we address the alignment issue inreading and in mathematics for a limited number of countries. Table 1: Overview of curricular materials obtained for each country/education system, by document type and subject* Official Curriculum At Least One Textbook in** Guideline or SyllabusRegion Country/Ed System Reading Mathematics Reading MathematicsArab States Egypt X X X Jordan X X X X Lebanon X X Libya X X Palestinian Autonomous X X Territories Qatar X Sudan (southern) X X Syrian Arab Republic X Tunisia X X X9 In addition, we have obtained a very small number of tests (4) and published articles (2).10 This number is higher (for reading) if we include the 5 Caribbean countries covered in one official Eastern Caribbean document.11 It is worth emphasizing that the number of documents compiled per country does not necessarily reveal the comprehensiveness of the information provided on the intended curriculum. For example, some countries have two textbooks for each grade (one per semester), or different textbooks for lessons and for exercises. Official curricular statements and guidelines can also be more or less comprehensive and detailed in the curricular information they contain. 10
    • United Arab Emirates X XCaribbean Bahamas X X X Bermuda X X Dominican Republic X X X X Eastern Caribbean*** X Jamaica X X Saint Lucia X X Trinidad and Tobago X X XEast Asia and the Pacific Cambodia X X X X China (all areas except X X X X Shanghai and Beijing) China, Shanghai only X X China, Beijing only X X Hong Kong X X X X Indonesia X X Papua New Guinea X Philippines X X X X Singapore X X X Taiwan X X X X Thailand X X X X Vietnam X X XLatin America Argentina X X X X Belize X Brazil X X X X Chile X X X X Colombia X X X X Costa Rica X X X X Ecuador X X X X El Salvador X X Guatemala X X X Mexico X X X X Nicaragua X X Panama X X Paraguay X X X X Peru X X X X Venezuela X XSouth and West Asia Afghanistan X Bangladesh X X X India X X Iran X X Pakistan X X X X Sri Lanka X X X XSub-Saharan Africa Angola X X Benin X Botswana X X 11
    • Ghana X X X X Lesotho X X Mauritius X X Namibia X X Senegal X X South Africa X X Uganda X X X XCentral Asia Armenia X X Kyrgyzstan X X Uzbekistan X XTotals 43**** 43 44 39Notes:* More country-specific information on the exact grade level(s) or grade range covered by documents in the Archive is available at http://www.albany.edu/eaps/international.shtml under ‗ICATA‘.** The number of archived textbooks and exercise books per country ranges from less than 4 in Ecuador, Bangladesh, Chile and Indonesia, to more than 20 in Pakistan, Hong Kong and Thailand.*** Refers to a regional document prepared by the Organisation of Eastern Caribbean States, Education Reform Unit for 5 countries (Antigua and Barbuda, Grenada, St. Kitts and Nevis, St. Lucia, St. Vincent and the Grenadines) and 4 territories: (Anguilla, British Virgin Islands, Dominica and Montserrat).**** Since this includes the Eastern Caribbean regional document, the actual number of countries for which curricular guidelines for reading exist is 45 (or including territories, 49).2. How representative and diverse are the curriculum materials in the international archive?As Table 1 indicates, curricular information—albeit partial--is currently available for asignificant number of developing countries in the following (sub)regions: the Arab States, theCaribbean, Latin America, East Asia, and South and West Asia. The collection of officialdocuments and textbooks for countries in Central Asia, sub-Saharan Africa (mainly francophoneAfrica), and the Pacific is less extensive.To address questions about the coverage, representativeness and diversity of the internationalarchive, the following tables compare select aspects of the cases included in the archive with alldeveloping countries. Comparisons are organized around the six UNESCO developing regions.Figure 1, for example, calculates the percentage of primary enrollments in each region that are‗covered‘ by country curricular materials in the archive. This comparison indicates that, inenrollment terms, the archive‘s coverage of the educational systems in East Asia (though not thePacific), Latin America and the Caribbean, and South and West Asia is very strong, butconsiderably less so for education systems in the Arab States and Central Asia and, least of all,for sub-Saharan Africa.Figure 1: Percentages of primary school enrolments in each region that are represented bycurriculum materials in the international archive* 12
    • 100% 90% 80% 70% Not covered 60% 50% Covered 93% 93% 98% 40% 30% 50% 20% 42% 10% 19% 0% Arab States Central Asia East Asia and Latin America South and Sub-Saharan the Pacific and the West Asia Africa Caribbean*Only primary enrolments in developing countries are included in the calculation of the regional ratios.Figure 2 examines the extent to which countries in the archive are similar to all developingcountries in each region, in terms of average per capita income or GNP. This comparisonindicates that average income levels of archived cases are representative of all countries in LatinAmerica, the Caribbean and South and West Asia. The archive tends to include a greaterpreponderance of lower income developing countries in three regions (i.e., the Arab States,Central Asia and East Asia and the Pacific) and of higher income countries in one region (sub-Saharan Africa).Figure 2: Weighted regional averages of GNP per capita (2007) for countries included in thearchive as compared to the average of all developing countries in the region 13
    • 12000 10142 9822 10000 7727 8000 Sample US$ (PPP) 6026 6026 6000 Region 5112 4719 4577 4000 2770 2929 2880 1888 2000 0 Arab States Central Asia East Asia and Latin America South and Sub-Saharan the Pacific and West Asia Africa CaribbeanEnsuring language diversity in the archived curricular materials was an important aim of thisstudy. All together, the project coded curriculum documents in 15 languages: Spanish, English,Arabic, Mandarin Chinese12, Urdu, Farsi, French, Portuguese, Thai, Bahasa Indonesian,Cambodian, Uzbek, Sinhala, Pashtu and Vietnamese. Language proficient coders were trained tocode textbooks and curricular materials in each of these languages. In only one language,Bangla, was the project unable to locate a suitable coder in a timely fashion. The distribution oflanguages found in the archived documents varies depending on document type (see Figure 3 forofficial guidelines and Figure 4 for textbooks). A comparison of the two frequency distributionsindicates that English and Spanish are more commonly used in the preparation of officialguidelines and curricular statements, whereas textbooks are much more likely to be written in awider array of national or official languages.Figure 3: The number of official curricular statements and guidelines in the international archive,by language12 Mandarin Chinese includes both traditional (Hong Kong, Taiwan) and simplified (China, Shanghai, Singapore) Mandarin. 14
    • 35 English 48 25 Spanish 30 5 Sinhala 5 Mandarin* 5 5 1 Arabic 3 Thai 2 CODED 2 Portuguese 0 2 2 TOTAL Khmer 2 Vietnamese 01 Urdu 1 1 French 01 0 10 20 30 40 50 60* Mandarin Chinese includes both the traditional (Hong Kong, Taiwan) and simplified (China, Singapore) forms.Figure 4: The number of textbooks and exercises in the international archive, by language 40 Mandarin* 79 49 Arabic 66 34 Spanish 65 English 41 57 Urdu 13 14 Thai 5 13 Vietnamese 10 10 Uzbek 6 6 CODED Portuguese 4 6 Khmer 6 TOTAL 6 French 2 6 Farsi 36 Bahasa Indonesian 6 6 Sinhala 4 5 1 Pashto 1 0 10 20 30 40 50 60 70 80 90* Mandarin Chinese includes both the traditional (Hong Kong, Taiwan) and simplified (China, Singapore) forms.In sum, while the curricular materials analyzed in this cross-national study do not constitute arandom or representative sample of all developing countries in the world, they do represent theofficial curricular intentions in some regions better than others. Specifically, the analyzed cases 15
    • provide a more representative picture of official policies and textbook contents in three regions:Latin America and the Caribbean, East Asia (though not the Pacific), and South and West Asia.More work will need to be done in the future to obtain materials from countries in the ArabStates, sub-Saharan Africa and Central Asia, in order to provide a more complete picture ofcurricular patterns in these regions.3. Developing a coding scheme to compare curricular documentsA central task of the present project was to develop and validate a coding scheme tosystematically record and compare the intended reading and mathematics curriculum in differentnational primary systems. As previously noted, the bulk of a country‘s curricular intentions andpolicies can be captured in two document types--official guidelines/syllabi/statements andsubject-specific textbooks. A ‗valid‘ coding scheme for this study entailed a coding scheme thatsystematically recorded the explicit or overt contents of these two document types.To be sure, textbooks and curricular materials can reflect multiple social, cultural, political andeducational ideas—for example, political philosophies, pedagogical theories, normative notionsof child development, gender roles, citizenship concepts, cultural values, etc. Much socialscience scholarship has highlighted the implicit or ‗hidden‘ contents of textbooks and thecurriculum. These studies have examined, for example, assumptions about gender, class, race,authority, morality, citizenship and what does (and does not) count as school ‗knowledge‘(Bowles and Gintis 1976; Dreeben 1968; Anyon 1980; Giroux and Purpel 1983; Lynch 1989). Inthe present study this scholarship was less relevant since the focus is on the overt and intentionalcontents of official guidelines and textbooks in the areas of reading/language or mathematics.With this in mind, we sought out a sufficiently detailed and comprehensive coding scheme,which would enable comparisons of contents across a diverse range of documents and countries.After considerable consultation and deliberation, it was decided to utilize (and later simplify) twopreviously elaborated coding frameworks--one for mathematics based on TIMSS, and the secondfor reading based on PIRLS.13 These coding frameworks define extremely detailed categories tocapture two central dimensions of the mathematics and reading curriculum: 1) the intendedtopics, issues and contents taught in each subject; and 2) the standards that students areexpected to attain in each subject at a given grade level (or cycle). The first dimension capturessubject knowledge domains while the latter refers to the skills and competences that students areexpected to perform (achieve) as a consequence of classroom instruction. These twodimensions—contents and performance expectations—became the basis for carrying outcomparisons across nationally authorized curriculum materials in reading and mathematics.One reason previous studies have used an extremely detailed coding scheme is to providerelevant information not only to comparative education researchers and policy makers, but alsoto textbook authors and curriculum developers. The current project, given its focus onidentifying core content commonalities across diverse developing countries, required lessdetailed coding schemes. For this reason, slightly simplified versions of the original codingframeworks were developed for mathematics and reading (for copies of the coding frameworks,go to: http://www.albany.edu/eaps/international.shtml and see ICATA).13 For more information about these two international learning assessments, see http://timss.bc.edu/ 16
    • The mathematics framework was divided into ten general content topics, which were dividedinto detailed sub-categories, and even sub-sub-categories. The topics ranged from simplemathematical concepts (e.g., whole numbers, fractions and decimals) and operations to morecomplex topics such as geometry, proportionality and data representation. To achieve uniformityand simplify the coding process the most detailed categories were excluded from the completedcoding forms.The performance expectations in the mathematics framework were organized in a similar way--from the simple to the more complex. Five basic performance expectations were considered:knowing, using routine procedures, investigating and problem solving, mathematical reasoning,and communicating. Each performance expectation was further subdivided into one or morespecific competencies. The most detailed level included a list of highly specific activities orabilities that can be identified and classified in each textbook or document.The reading framework initially detailed the types of written texts that students are expected tostudy, including their elements and purposes. This initial category elaborated over 60 types ofwritten texts including, for example, a story, fable, proverb, letter, essay, joke, personal diary,poem, form, report, editorial, play, novel, manual, news item, comics, catalog, definition, sign,invitation and biography. The next dimension of the reading framework concentrated on specificelements of written texts—for example, their structure and functions. In most categories three orfour levels of specificity were provided in order to achieve uniformity and be inclusive of alltopics contained in the reading documents and textbooks.The performance expectations in the reading framework were divided by level of readingcomprehension, beginning with the most basic form--identifying parts in the text. Overall,performance standards were divided into four categories: literal comprehension, inferentialcomprehension, value or evaluative comprehension, and meta-comprehension. Each of thesecategories included a brief description of the more specific proficiencies that students wereexpected to achieve.4. Language issuesLanguage poses a singular challenge in this cross-national curriculum study, given the variety oflanguages in which archived documents are written. In the 1990s similar challenges were facedin the TIMSS Curriculum Analysis project--a large-scale international content analysis of officialcurricular documents (Schmidt et al. 1997; Survey of Mathematics and Science Opportunities1992, 1992, 1993; Valverde et al. 2002)--from which the present study drew insights.In broad terms, a close adherence to the original language of the documents to be coded hasdistinct advantages--primarily in terms of authenticity, accuracy and minimizing sources of error.For this project, which sought to identify substantive commonalities among diverse reading andmathematics curricula, it was important to read (or carefully skim) the entire contents of eachdocument or textbook. As such, translating and coding the ‗table of contents‘ or summaryexercises at the end of chapters would have biased the identification of commonalities. Indeed,translating documents into a common international language, in additional to the time and 17
    • expense involved, raises many methodological and substantive questions: Is the translationaccurate? Does it capture the intended meaning of the original text? Does the coder of thetranslated text understand the subtleties of the reading and mathematics activities described inthe original text? Might coders tend to over-estimate what is common across diverse texts whenthey are read or coded in a common international language? Comparative education researchershave generated different responses to these issues (e.g., Goldstein 2004; Puchammer 2007). Texttranslation, more often than not, creates new sources of inaccuracies and error, which this projectsought to minimize. Thus, to avoid these and other translation-related pitfalls, it was decided tomake every attempt to stick closely to the original language. Consequently, the project expendedsubstantial time on identifying language proficient coders, assuring quality training to enhanceinter-coder reliability and closely monitoring language ‗problems‘ during weekly meetings.5. Document profiles resulting from the coding process14Official curricular documents and textbooks are intricate and often lengthy. Special codingschema and procedures were developed to analyze their complex contents in order to create asuccinct, document-specific profile. To this end, coders began by dividing each document into adiscrete number of ‗segments‘ for analysis, often following the organization of topical contentsfound in the document itself. Each segment served as a functional portion or section of thedocument, which could be coded using the mathematics or reading coding framework. Toachieve consistency across different document types in the same country, and acceptable levelsof comparability across documents from different countries, the project research team initiallyhad two or more coders delineate ‗segments‘ of analysis in a sample of documents. Only whenan agreement was reached on the rules for identifying the analysis segments of documents, didthe actual coding process begin. This procedure often required informal translations of somedocuments so that several coders could consider materials written in languages in which theylacked proficiency.The main coding procedure involved identifying the contents, performance expectations--and, inthe case of reading, types of text--found in, or relevant to, each functional ‗segment‘ of a givencurriculum statement or textbook. Coders read each segment and then assigned to each one aseries of number codes from either the reading or mathematics framework. These codes becamethe main source of recorded data, and the basis for characterizing and comparing officialdocuments. For example, a 4th grade mathematics textbook might have 10 segments, most ofwhich were assigned codes from the categories of whole numbers, operations, decimals andfractions. At a different grade level, or in a country that has undergone curricular reforms inmathematics, the analyzed textbook might have an equal number of segments, but somesegments focus on topics like proportionality, statistics and elementary geometry and thusreceive other codes. Or consider an example from reading: one national policy document(curricular guideline) may call on students to be exposed to a wide array of text types (e.g.,brochures, itineraries, letters, biographies, poems, stories, electronic correspondence), whileanother might specify fewer text types, indicating, perhaps, that students are intended to workprimarily with short stories and information-oriented articles.14 The techniques briefly described here have been extensively reported in the literature on empirical studies in curriculum (Cogan, Wang, and Schmidt 2001; Robitaille et al. 1993; Schmidt et al. 1996; Schmidt et al. 1997; Survey of Mathematics and Science Opportunities 1993, 1993; Valverde 2000, 2002, 2005; Valverde et al. 2002; Valverde and Schmidt 2000). 18
    • Once the coding process was completed, a set of specific content and performance expectationcodes came to be associated with each document. Document profiles (strings of content andperformance codes) were then aggregated within and across grade levels to describe the intendedreading or mathematics curriculum of a country. During the next phase, various analyses wereperformed, basically involving a comparison of document profiles across—and sometimeswithin--countries. For example, to determine commonalities in the intended curriculum wecompared aggregated national profiles by subject and document type. We set a benchmark of70% to decide whether a particular content item (or performance expectation) was ―common‖ ornot (see below). (In other words the same code needed to appear in at least 70% of the countrieswith documents of certain type). In other analyses we compared whether the same codes werefound in curricular guidelines and textbooks in the same country (the alignment issue discussedbelow). In still other analyses we calculated and compared the proportion of segments in whichparticularly ―challenging‖ mathematics codes were identified in documents. In sum, all theanalyses performed relied, first and foremost, on the creation of a single profile for a givencurriculum statement or textbook at a given grade level.6. Quality assurance in coding proceduresIn a large-scale, multi-lingual project such as this, quality assurance was especially important.This study introduced several modifications to the aforementioned TIMSS coding methodology,resulting in procedures that endeavored to balance measurement rigor with efficiency. Animportant difference between the TIMSS coding procedures and the present study was that alltraining and coding was carried out at a central location (the University at Albany-SUNY). Theoriginal TIMSS procedures used a ―training of trainers‖ formula, with a set of quality controlprocedures at the beginning and the end of the data collection period, with coding occurring inmultiple locations around the world.In the current project, an initial one-week training and quality assurance session was convened,which brought local graduate students together with textbook and curriculum experts–all withcomplementary languages proficiencies. Standard training materials developed for the TIMSSproject, and extended by the Educational Evaluation Research Consortium (Valverde 2003) forreading, were used to familiarize coders with the full set of project procedures. These initialmeetings used standardized presentations, training-to-criterion exercises, and authentic curricularmaterials from a number of languages and countries across the world to build a commonunderstanding of the document analysis procedures. When coders evidenced sufficient criterionconcordance with the content experts on the team, they were assigned country documents in linewith their language proficiencies and the main coding process began.Given that the coding procedures were fairly demanding, several mechanisms were establishedto ensure the entry of high quality, reliable and valid data. These included the face-to-facetraining of new coders, an initial assessment of coding reliability and careful on-goingmonitoring of the resultant document profiles. In addition, the team held regular weeklymeetings with the project‘s Principal Investigator, consultants, and coding staff during whichgroup consultations were conducted about specific coding issues as well as the assignment ofnew documents as they arrived. For documents in languages beyond the proficiencies of team 19
    • members, new student-coders were identified and trained in the use of both subject frameworks.During an initial training phase, the trainees carried out a series of common exercises, and beganthe coding exercise only after more experienced coding referees were satisfied that they hadachieved sufficient command of the procedures.7. Creating ‗master tables‘ of profiles and setting benchmarks to establish ‗commonalities‘As the project progressed more and more curricular documents were coded, thereby increasingthe number and diversity of national curricular profiles in reading and mathematics. Obviously, itmade little sense to search for commonalities among all document profiles in the collectionsince, for example, the reading and mathematics profiles were based on entirely different codingframeworks. Less obvious, but no less important, was whether to combine analyses of differentdocument types (i.e., official guidelines and textbooks). Given substantive differences in thepurposes, scope, target audiences and uses of the two main document types, it was decided toconduct separate searches for commonalities among curricular guideline profiles, on the onehand, and textbook profiles, on the other.Another issue to emerge related to the primary grade levels to be compared. Due to timeconstraints, the project only coded and compared documents from grades 5 and 6 (see below).However a question arose whether to compare the curricular intentions of grade 5 and grade 6separately, or in some combined fashion. In reality, some countries require instruction in, forexample, geometry or proportionality in grade 5 while others do so in grade 6. In both cases thetopic is required knowledge by the end of the primary cycle. Thus, to be able to draw validinferences for certain analyses, it made sense to pool curricular information across both gradelevels. With this in mind, separate analyses of commonalities were carried out on grade 6documents only--the modal final grade of primary education in most developing countries (UIS2008:28); and then on the ‗accumulated‘ or pooled contents and performance expectations ofdocuments for both grade 5 and grade 6.15 As expected, the resulting lists of commonalities inmathematics and reading tend to be longer when information is pooled for both grades 5 and 6 ascompared to grade 6 only.The aforementioned decisions resulted in a 2 X 2 X 2 matrix of analysis (see Figure 5) by subject(mathematics and reading), document type (curriculum guideline and textbook) and grade level(grade 6 only vs. grades 5 and 6 combined). In practice, all coded profiles were first categorizedby subject and document type. When information existed for both grades 5 and 6, then a new‗pooled‘ profile was created, which combined information for the two grades.16In the end the search for commonalities involved comparisons of country profiles within eight‗master tables‘--four in mathematics and four in reading. A question arose as to the criterion or15 A country profile for grades 5 and 6 means that the codes for grade 5 and grade 6 documents have been pooled, so that the resulting profile lists contents and performance standards that were found in grade 5 and/or grade 6. In addition, while the project has compiled quite a number of grade 4 documents, most remain to be coded. In the future it may be possible to include grade 4 materials.16 The actual statistical profile of a country’s intended curriculum (by subject and document type) is based on proportions (i.e., the number of segments in which a specific content category occurs). For the purpose of the present study, these proportions were transformed into dichotomous variables: in other words, the content category (or performance standard) was either present (or not) in the official document. 20
    • benchmark that should be used to determine whether specific content areas were held in‗common‘ in each master table. What percentage of countries in each master table should share acommon content or performance code in order to determine a state of ‗commonality‘? Using pastresearch as a guide (Schmidt et al. 1997) it was decided to employ a benchmark of 70%—inother words, a specific topic or performance expectation in reading or mathematics was deemedto be held ‗in common‘, if it was present in at least 70% of the developing countries listed in amaster table.That said, if a master table contained too few country profiles (say, less than 10), then validinferences concerning commonalities would be questionable. We set a target of at least 15(diverse) countries per master table to apply the 70% benchmark. In fact this target wassurpassed in every table. As Figure 5 reports, the actual number of countries included in the eightmaster tables ranged from 23 to 33; the average is 28.8.Figure 5: Number of countries in each of the eight ‗master tables‘ SubjectDocument types Mathematics Reading Grade 6 (only) 27 23 Curriculum Guidelines Grades 5 & 6 30 25 Grade 6 (only) 33 32 Textbooks Grades 5 & 6 31 29 VI. ResultsThis section reports results that address three major research questions:To what extent do diverse developing countries in the world define similar contents andperformance expectations in reading and mathematics in the upper grades of primary education?(the commonalities issue)To what extent do the content domains of official curriculum statements in reading andmathematics align with those found in relevant textbooks? (the alignment issue)In which countries are performance expectations in mathematics curricula more (or less)cognitively challenging?17 (the challenging curriculum issue)17 In the future we hope to examine the same question in the area of reading. 21
    • 1. Commonalities in the intended curricula of developing countriesTo aid the reader in the identification of commonalities, eight tables (Tables 2 thru 9 appendedbelow) have been constructed that list only those codes (or detailed categories) of contents andperformance expectations in mathematics and reading that are shared by 70% of the countries.18Stated differently: if a content topic or performance expectation (or, in the case of reading, typeof text) is not listed in one of the tables, this means that it was not present in at least 70% of thecountries and thus not considered a common curricular element.For mathematics the key findings can be summarized as follows: As expected, the list of common mathematics contents and performance standards is longer when information for two grade levels (5 and 6) is pooled rather than for just one grade level (grade 6). This pattern obtains both with respect to textbooks (Table 3 as compared to Table 2) as well as curricular statements (Table 5 as compared to Table 4). The list of country commonalities in mathematics is shorter when comparing official curriculum statements/guidelines than when comparing textbooks (Table 4 vs. Table 2 or Table 5 vs. Table 3). In general, curricular guidelines in mathematics, which target teachers, school administrators, principals and inspectors, vary to a greater extent across countries in their detail and specificity than textbooks. Divergent country views of what should be included in official statements/guidelines create a less cohesive picture of the intended mathematics curriculum of developing countries. Thus, when these types of documents are compared, the picture to emerge is one of fewer commonalities in mathematics. Among the large and diverse array of mathematics textbooks analyzed in this study, there is a surprising number of common contents and performance expectations. This is apparent both in Table 2 (which only examines grade 6 textbooks) and Table 3 (which pools information from textbooks used in either grade 5 or grade 6). Focusing on Table 3, more than 70% of the developing countries studied use textbooks that include instruction in: whole numbers, fractions and decimals; number theory; measurement units and issues; one-, two- and three-dimensional geometry; proportionality concepts and problems; and data representation (though not probability and statistics). Missing from this list are, for example, advanced mathematical topics in geometry; functions, relations and equations; elementary analysis; validation and structure; and probability and statistics. Overall, there are many commonalities in the content domains of grades 5 and 6 mathematics, as least as reflected in the textbooks analyzed in this study. Both textbooks and official curricular guidelines also contain many shared performance expectations in mathematics--for example, representing mathematics expressions and18 Only categories with numerical codes were coded and these constitute the basis for determining commonalities in each table. The sub categories within these categories that lack such codes were used mainly to help coders understand the content of each numerical category. 22
    • recognizing equivalents; using measuring instruments; performing various kinds ofcounting, computing, graphing and measuring procedures; using more complexprocedures (estimating and collecting data and classifying objects); and investigating(formulating mathematics statements to represent real world situations) and problemsolving.Missing from the lists of commonalities are the more challenging performanceexpectations: all types of mathematical reasoning as well as competences related to usingmathematical vocabulary and notation; relating representations; and describing,discussing and critiquing written and verbal statements/expressions in mathematics. Twoaspects of investigating and problem-solving (i.e., predicting, and verifying) are alsomissing from these lists. Overall, commonalities in performance expectations mainlyrevolve around routine and basic skills in mathematical problem solving and reasoning,and not in relation to the more cognitively demanding skills.Several elements are of particular interest in the list of shared mathematics topics.Whereas some topics have traditionally been part of primary mathematics curriculum fordecades (e.g., whole numbers, fractions and basic geometry), other topics reflectcontemporary reforms in mathematics curricula (e.g., topics in ‗data representation andanalysis‘). Collecting data, arraying them in simple tables and graphs, understandingsimple measures of central tendency and dispersion, and sampling—all these are topicsthat represent recent reform trends in mathematics curricula, and are currently found in awide array of developing country textbooks and official guidelines. In fact, many of thesetopics have only recently entered pre-service teacher training programs worldwide (Mills2007; Mullens et al. 1996; Philipp 2008; Wilburne and Napoli 2008). Thus, the findingssuggest that the reform dynamic in mathematics education has impacted a broad spectrumof developing countries, which have not been the subject of sustained empirical study.Many such countries are in agreement as to the merit of this type of challenging contentin the upper grades of primary education.Another reform-oriented topic—‗proportionality‘—garners broad presence in uppergrade textbooks, but not in official intended curricular policies. Proportionality and theattendant topics in the area of fractions represent some of the most abstract andchallenging subjects in primary school mathematics. They are considered vital todeveloping strong mathematical reasoning skills. Indeed, many experts agree that thesetopics represent the most cognitively demanding subjects in the primary schoolcurriculum: often equally challenging for students and their teachers. A number ofauthors observe that common and decimal fractions are the first serious exercises in thetype of abstract mathematical reasoning that students will have to master if they wish tobecome perform well in Algebra courses (Irwin and Irwin 2005; Jeong, Levine, andHuttenlocher 2007; Noddings 2009; Pagni 2004; Simon 2006; University 2006). Thefindings suggest that while textbook authors and editors agree on the importance ofproportionality and related topics, formulators of official curriculum policy in thesecountries do not. 23
    • Other findings further illustrate the divergent perspectives of the authors of official policy statements and those of mathematics textbooks. For example, in the area of performance expectations, curriculum statements in mathematics commonly call for the inclusion of cognitively more complex performances in such areas as ‗estimating data‘ or ‗formulating and clarifying problems and situations‘ (e.g., using mathematical expressions to represent real world problems). These competences, which are more demanding than routine procedural knowledge and algorithms, require more challenging learning opportunities (Blair, Knipe, and Gamson 2008; Buxkemper and Hartfiel 2003; Callingham and Watson 2004; de Castro 2008; van Oers and Poland 2007). Performance expectations of these types are more likely to be absent in official guidelines, but present in textbooks, thus raising concerns from a curriculum policy perspective.In the area of reading the main findings from Tables 6 through 9 can be summarized as follows: Developing countries clearly hold divergent views about the contents of the upper grade primary reading curriculum. The findings point to many fewer commonalities across a wide range of texts, topics and contents areas in the reading curriculum for grades 5 and 6. This is especially true in relation to official policy statements and guidelines and a bit less so from the perspective of textbooks. The contrast with the intended mathematics curriculum is quite stark. Two patterns of results are similar across both subject areas. First, as in mathematics, the list of common contents and performance standards in reading is longer when information for two grade levels (5 and 6) is pooled rather than just one grade level (grade 6). This pattern holds not only with respect to textbooks (Table 7 vs. Table 6), but also curricular statements (Table 9 vs. Table 8). Second, the list of commonalities in reading is longer when examining textbooks as compared with official curriculum guidelines (contrast Table 6 with Table 8 and Table 7 with Table 9). Again we see that the specificity required of textbooks engenders greater common contents. Several findings concerning the contents of reading are especially noteworthy. First, textbook authors apparently draw upon a wide array of text types to help students develop their reading proficiency skills. From a list of over 60 types of written texts, only 6 were found in at least 70% of the grade 5 and grade 6 textbooks examined. These included: stories/tales, poems, plays, letters, historical accounts and biographies. (In grade 6 textbooks, only the first two types of written texts are commonly found). Second, according to the analyzed curricular guidelines there is only one type of written text— poems--that 70% of the 25 developing countries viewed as necessary to be included in the upper primary reading curriculum. Thus, policy analysts and ministry officials around the developing world hold few common views concerning the types of text that students are expected to utilize, when acquiring or strengthening their reading proficiency in an official language.1919 The languages examined in the curricular guidelines for reading included, among others, Spanish, Urdu, English, Singhalese, Mandarin Chinese, Thai and Cambodian. 24
    • Only one basic element of reading is common to both textbooks and curriculum guidelines—namely, including a written text whose function is to be informative. Thus it appears that official curricular guidelines in reading are rather general documents lacking specification, and that the authors of such guidelines and those of textbooks utilize different vantage points when defining the structure and purposes of written texts that primary students are expected to learn. Focusing solely on textbook contents for grades 5 and 6, comparisons across countries indicate a slightly increased number of commonly held elements. For example, most textbooks include written texts that: 1) have plot types emphasizing narration, description, explanation and exposition; 2) include acts of speech involving a dialogue between two individuals; and 3) help students to identify different plot elements (e.g., who does what to whom for what reasons, as well as the first, second, or third person viewpoint of the narrative). Most textbooks also provide explicit instructions to students about the different modes by which texts should be read: by reading them out loud, in silence, and by scanning or skimming them. All of the above elements of the intended reading curriculum were commonly found in over 70% of the grade 5 and 6 textbooks studied, although they are more rarely found in official statements. With respect to reading skills/competences that students are expected to achieve in the latter grades of primary education, the cross-national evidence indicates considerably more commonalities. For example, more than 70% of textbooks and guidelines agree that students should: 1) identify, extract, find and remember explicit information in the written text; 2) develop inferential skills to compare, deduce, generalize, apply, interpret, connect, summarize and paraphrase implicit elements in the text; and 3) develop a range of evaluative judgments about the texts they read (e.g., the extent to which the texts are coherent/incoherent, precise/vague, complex/simple, valid, reliable, complete, plausible). These findings indicate that, despite pronounced cultural and linguistic differences, many developing countries share common ideas as to the desired reading standards by the end of the primary cycle. These commonalities are known as literal comprehension, inferential comprehension and value or evaluative comprehension. A fourth element known as ‗meta-comprehension‘—encompassing, for example, the abilities to formulate and prove hypotheses, make predictions, continue reading, develop analogies and identify antecedents to the text—is only found to be common in reading textbooks. 2. Alignment between curricular intentions and textbooksOver the years the international assessment literature has emphasized a key distinction betweenthe official, intended curriculum (what should be taught) and the actual, implemented curriculum(what is actually taught). While comparative information about the former is fairly abundant,systematic evidence about the latter is considerably less so. This stems, in part, from the fact thatdifferent conceptions and measurement strategies have been developed to capture theimplemented curriculum (e.g., Rosier and Keeves 1991; Resh and Benavot 2009). The argumenttypically put forward is that student achievement levels will be higher or will increase, ineducational contexts where the intended curriculum and the implemented curriculum are moreclosely aligned. This issue is especially salient in the developing world where many sources 25
    • describe serious gaps or slippages between the two, mainly in terms of instructional time,textbook availability, and the like (Abadzi 2007; GMR 2007b).In this study, curricular guidelines and statements accurately represent the official intendedcurriculum in each subject. By contrast, as previously noted, textbooks provide an incompleteand inconsistent picture of the actual implemented curriculum. In those settings where teachersorganize their class lessons in close accordance with textbooks, then textbooks more closelyapproximate the actual implemented curriculum. But this tendency varies greatly betweenclassrooms, schools and regions, especially in developing countries. Therefore it seems morefitting to refer to textbooks as an instructional device that mediates policy intentions andcurricular implementation (Valverde et al. 2002).For a limited number of countries and provinces this study compiled analogous profiles of thecontents of official guidelines and textbooks in mathematics and reading. By comparing theprofiles of curricular guidelines to those of textbooks in the same country or province, we canascertain the extent to which contents between the two documents are shared or ‗in alignment‘.In operational terms when the same content codes appear in the profiles of both types ofdocuments, then a high level of alignment can be said to characterize the country or system. Inthe analysis below, actual percentages are calculated by dividing the total number of sharedcodes found in both country documents (pooling information for grades 5 and 6) by the totalnumber of content codes found in the coding framework for each subject. The guideline-textbookalignment analysis in mathematics includes 10 countries and, for the case Pakistan, 3 separateregions (Figure 6); it involves 12 countries in the area of reading (Figure 7).Figure 6: Alignment between the official curriculum and textbooks in mathematics, grades 5 & 6 Percentage of aligned contents between the official curriculum and textbooks in mathematics in grades 5 and 6, by country or system Thailand 38.6% Cambodia 36.8% Costa Rica 35.1% Phillipines 33.3% Taiwan 31.6% Hong Kong* 31.6% Dominican Republic 31.6% China 29.8% Peru 28.1% Argentina 26.3% Pakistan**- Sindh 19.3% Pakistan**- Punjab 17.5% Pakistan**- Khyber-PakhtoonKhwa 15.8% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 26
    • * The comparison is between the official curriculum in grades 4-6 and the mathematics textbooks in grades 5 and 6.** The comparison is only between grade 5 curriculum and grade 5 textbooks.Figure 7: Alignment between the official curriculum and textbooks in reading, grades 5 & 6 Percentage of aligned contents between the official curriculum and textbooks in reading in grades 5 and 6, by country Pakistan** 55.6% Cambodia 38.7% Mexico 30.6% Phillipines 29.8% Dominican Republic 22.6% Hong Kong* 21.8% Taiwan 19.4% Paraguay 18.5% Colombia 16.1% Costa Rica 12.9% Bahamas 12.1% Thailand 8.9% 0% 10% 20% 30% 40% 50% 60%* The comparison is between the official curriculum in grades 4-6 and the mathematics textbooks in grades 5 and 6.** The comparison is between the curriculum for grades 5 and 6 and textbooks used in grades 4 and 5.Several interesting patterns can be discerned in these figures. First, setting aside the unusual caseof Pakistan, estimated alignment levels—that is, the percentage of shared contents betweencurricular policies and textbooks—are quite low. In mathematics, they range from a high of 39%in Thailand to a low of 26% in Argentina; in reading they range from 39% in Cambodia to 9% inThailand. In all of the developing countries studied, official curricular policy documents andtextbooks share less than 40% of the same contents. There is little indication that grade 5 and 6textbook authors follow closely the explicit official policy directives in devising textbookscontents in mathematics and reading. Second, the percentage of aligned contents tends to behigher on average in mathematics than in reading. Not only are there more commonalities inmathematics than in reading across diverse developing countries, as previously shown, but thereis also a closer alignment within countries between the intended and potentially implementedcurriculum in mathematics.Third, in some countries relatively higher alignment levels are found in both mathematics andreading: Cambodia, Philippines and, to a lesser extent, Hong Kong, Taiwan and the DominicanRepublic. In other countries, the alignment levels vary by subject—for example, in Thailand arelatively high alignment in mathematics contrasts with a low one in reading. A similar patterncan be seen in Costa Rica. Additional evidence is needed before one can infer that tighteralignment between intended curricular policy and textbook contents mainly reflects (centralized)government coordination and stakeholder communication or whether alignment patterns vary 27
    • more systematically by school subject. Finally, in the case of Pakistan, mathematics alignmentlevels are similar--and low--between official policy statements and each of three grade 5mathematics textbooks used in different parts of the country (Sindh, Punjab and Khyber-PakhtoonKhwa). By contrast, the level of alignment in reading is exceptionally high in Pakistan. 3. Establishing challenging standards in mathematics curriculaThe drive to reform the school curriculum in the developing world often revolves around thetypes of knowledge, competences and values that students are expected to obtain by thecompletion of primary or basic education. Some countries focus on the mastery of basic skills inliteracy and numeracy; in others educational leaders want primary schools to expose students,especially in the upper grades, to more complex and challenging contents, as a basis fordeveloping higher-order cognitive skills and related learning outcomes.In this study, the coding of performance expectations in mathematics guidelines and textbooksenabled us to identify more or less cognitively challenging curricula in different countries.20Drawing on related research in the area of mathematics (Schmidt et al. 1997; Brown, Schiller,and Roey 2010), all codes for performance expectations were re-classified to identify a subset ofcodes that denote the most cognitively demanding curricular standards. Specifically, 8 of 21three-digit performance codes in mathematics were singled out since they entail higher-ordercognitive reasoning and a broad set of problem solving strategies. Some codes denote thatstudents should develop problem-solving strategies that go beyond simple procedures and beable to identify the steps or methods to finding a solution to a mathematical problem. Anothercode implies that students should consider alternative ways of solving problems utilizingtechniques taught in the classroom and develop algorithms to solve similar problems in othercontexts. Two other skills—‗identifying or stating an appropriate conjecture or drawing anappropriate conclusion in the discussion of a mathematical idea‘ and ‗recognizing, selecting andpresenting a counterexample that demonstrates that a proposition is not true‘ also represent morechallenging performance expectations. In general, documents that contain a higher proportion ofthese cognitively challenging skills are indicative of policies that expect students to develop adeeper understanding of problem solving in mathematics, prove and justify their answers tomathematics problems, and see mathematics applications and connections outside the classroom.To identify countries that emphasize cognitively challenging standards a scale was constructedfrom the eight performance expectations noted above. If one of these eight codes appeared in adocument segment, even once, then it was counted as present (or one). Then for eachdocument—either a textbook or a curriculum guideline--the total number of such codes wassummed and divided by the total number of segments in the document. The scale ranges from 0to 1.0. A country scoring 1.0 means that all segments in a coded document included at least onecognitively demanding performance expectation. If a country stipulated more than one documentin the intended curriculum (e.g., two semester-length mathematics textbooks), then the totalnumber of performance expectations was divided by the total number of segments in all relevantdocuments. Analyses were conducted separately for grade 5 and grade 6 documents,21 in part toascertain whether documents in the higher grade have increased proportions of cognitively20 In the future it is hoped that similar analyses can be conducted in reading.21 In the cases of St. Lucia and Pakistan grades 4 and 5 are compared instead of grades 5 and 6. 28
    • demanding performance expectations. Figure 8 examines cross-national differences based on ananalysis of mathematics guidelines Figure 9 examines such differences based on textbooks.Figure 8: The emphasis placed on cognitively challenging performance standards in mathematicsguidelines, by country and grade level 1.20 1.00 1.00 1.00 1.001.00 1.00 1.00 1.00 0.89 0.83 0.86 0.80 0.78 0.75 0.75 0.80 0.70 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.71 0.62 0.60 0.60 0.60 0.60 0.60 0.56 0.57 0.60 0.50 0.50 0.50 0.50 0.45 0.43 0.42 0.38 0.40 0.38 0.40 0.32 0.20 0.00 Curriculum- 5th Grade Curriculum - 6th GradeFigure 9: The emphasis placed on cognitively challenging performance standards in mathematicstextbooks, by country and grade level 29
    • 1.20 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.93 0.95 0.89 0.89 0.88 0.88 0.90 0.86 0.83 0.81 0.79 0.80 0.75 0.78 0.75 0.80 0.71 0.72 0.73 0.70 0.67 0.67 0.67 0.64 0.63 0.57 0.57 0.60 0.35 0.40 0.150.14 0.20 0.11 0.00 Textbook - 5th Grade Textbook - 6th GradeTwo clear patterns emerge from these analyses. First, the prevalence of cognitively challengingmathematics curriculum and textbooks varies considerably across countries both in grade 5 andin grade 6. In some countries—for example, Guatemala, Bermuda, Costa Rica, Chile andThailand--a high proportion of demanding performance expectations are present in officialguidelines for both grades 5 and 6. The same is true for an even larger number of countries inrelation to their mathematics textbooks. By contrast, some countries include relatively fewcognitively challenging performance codes in their guidelines (e.g., Sri Lanka, Belize, Jamaica,Botswana, El Salvador) or in their textbooks (Cambodia, St. Lucia).Second, there is a tendency for performance standards to increase by grade level. This is moreapparent among mathematics textbooks--in 13 out of 20 countries the proportion of challengingexpectations increased from grade 5 to grade 6—but is also apparent in official guidelines whereincreases are found in 12 out of 21 countries. In some countries (e.g., El Salvador, Colombia inguidelines; Costa Rica and Pakistan in textbooks) the change between grade 5 and grade 6 issubstantial. By contrast, in many other countries the prevalence of cognitively challengingstandards changes little between the 5th and 6th grades. In some countries, it actually declines: forexample in relation to guidelines in the Bahamas, Taiwan and Bermuda and in relation totextbooks in Indonesia, Mexico and Egypt. Overall the analyses indicate that the intendedmathematics curriculum in many developing countries contains a large proportion of cognitivelychallenging materials, and this tends to increase in higher grades.In the future, once the coding of grade 4 documents has progressed, this grade-related tendencycan be examined more carefully. Furthermore, it would be germane to examine possiblerelationships between the structure of basic education and variations across countries and gradelevels in the prevalence of cognitively challenging standards in mathematics. For example, doesthe structuring of grade 6 at the end of the primary cycle or at the beginning of the lower 30
    • secondary cycle (or a third stage of basic education) influence the prevalence of cognitivechallenging expectations in the mathematics curriculum?Perhaps, more importantly, questions concerning the link with learning outcomes will need to beconsidered. Do countries that define more challenging performance expectations in either theirofficial guidelines or their textbooks succeed in facilitating higher student achievement inmathematics? Or, do more demanding curricular policies place unnecessary or unwantedobstacles in front of teachers and school directors, many of who struggle to inculcate basiccompetences in literacy and numeracy and seek to minimize student repetition and to maximizecompletion rates in primary education and higher transition rates to secondary education? Theseimportant questions deserve further scrutiny, as they cannot be addressed in the framework of thepresent study. VII. Discussion and concluding remarksThis report gives a comprehensive account of work activities completed in conjunction with thecommissioned study ‗Cross-national Commonalities and Differences in the Intended Curriculumin Primary School Reading and Mathematics.‘ The study‘s primary purpose was to compile,analyze and describe commonalities and differences in the intended (upper grade) primarycurriculum in reading and mathematics across a diverse set of developing countries. Beyond this,the study also addressed two related issues. The first issue—the alignment issue--explored theextent to which the contents of official curricular statements/guidelines and authorized textbooksare aligned with one another in the same country. The second issue identified developingcountries that have established relatively high or cognitively demanding performanceexpectations in mathematics for those students who complete 6 years of primary schooling.This study and the results reported herein are meant to fill a knowledge gap in currentinternational policy discussions concerning the intended contents and standards of the readingand mathematics curriculum in the developing world. By comparing curricular policies anddocuments in reading and mathematics in a diverse range of developing countries, it provides anew evidentiary base from which to discuss alternative strategies to improve the skills andproficiencies that students should acquire by the end of the primary cycle. It is hoped that thisstudy will contribute to on-going policy exchanges on quality education among different nationaland international stakeholders. Several concluding observations, including possible implicationsfor improving learning assessments in the developing world, are discussed below.With respect to mathematics, the findings indicated that the developing countries in this studyhold a fairly consensual and detailed view of what should constitute the mathematics curriculumin the upper grades of primary education—both in terms of contents and performance standards.Long lists of commonalities in the intended mathematics curriculum were apparent in bothdocument types—albeit more so among textbooks than official statements. These included coreelements of primary level mathematics: whole numbers, fractions and decimals; number theory;measurement issues; one-, two- and three-dimensional geometry; proportionality concepts andproblems; and data representation (though not probability and statistics). Also noteworthy wasthe presence of select ―reform-oriented‖ mathematics topics—for example, ‗data representationand analysis‘ and (in textbooks) ‗proportionality‘--in the intended curriculum of many primary 31
    • school systems in this study. This suggested an on-going trend: the growing diffusion andinstitutionalization of select curricular reforms in mathematics in the educational policyenvironments of many developing countries.The analyses in this report also highlighted many common performance expectations inmathematics across countries and document types. These shared standards mainly revolvedaround routine and basic skills in mathematical problem solving and reasoning (e.g., representingmathematics expressions and recognizing equivalents; using measuring instruments; performingvarious kinds of counting, computing, graphing and measuring procedures) and did not includemore cognitively demanding mathematics skills.With respect to the reading curriculum, a more fragmented—some would say, heterogeneous--picture emerged. Very few countries agreed on the types of written texts that should be usedwhen teaching reading. Only 6 of 60 different types of texts (i.e., stories/tales, poems, plays,letters, historical accounts and biographies) were found to be present in at least 70% of the uppergrade reading textbooks analyzed. There was also evidence of minimal agreement concerning theintended contents and structure of the upper primary reading curriculum. Divergent views wereuncovered: 1) across grade levels within countries; 2) between official curricular statements andtextbooks within countries; and 3) among the official documents of different developingcountries. (In the future possible commonalities among countries sharing a common language—for example, Spanish or Arabic—should be examined).Performance standards represented the one notable realm of the reading curriculum, in which aclear set of commonalities did in fact emerge. Common performance expectations specificallypertained to literal, inferential and evaluative forms of comprehension. The findings suggest thatthe developing countries in this study share a fairly common notion as to the kinds of readingcompetences students should attain by the end of the primary cycle, but have different views ofwhat constitutes the substance of the reading curriculum.Several possible explanations for these patterns come to mind. Mathematics is considered bymany to be a scholarly field containing a relatively well-defined and integrated knowledgestructure, in which different knowledge domains are tightly inter-connected and sequenced. Assuch, one would expect greater specification of which topics and contents are normally taught inprimary school mathematics, and in what sequence, than in other scholarly fields. Some scholarswould contend that international networks are denser and expert exchanges more frequent in thefield of school mathematics than in reading education. This would make it more likely thattextbook authors and editors would develop a more definitive understanding of the contents of a‗proper‘ mathematics curriculum. These propositions help explain the greater consensus amongdeveloping countries regarding the contents of primary level mathematics in contrast to reading.Another explanation entails the more universal ‗language‘ of mathematics versus the moreculturally embedded process of acquiring literacy skills and competences in an official nationallanguage(s). Without denying the cultural meanings embedded in mathematics, in reading suchelements are considerably more explicit. Shared historical experiences and prominent culturalfigures (or heroes) are likely to influence which authors and texts are chosen to teach in primaryschools. Perhaps surprisingly, these choices also appear to impact the characters and plots 32
    • deemed appropriate for primary students, the background information needed to comprehend andinterpret the texts and so on. Few of the developing countries in this study shared a commonnotion of what elements should be included in the reading curriculum of the upper grades ofprimary education. The findings underscore the extent of divergent views concerning the basiccontents of reading (types of written texts, acts of speech, plot types, etc.). Nevertheless,developing countries do hold common views concerning the type of skills and proficiencies thatthey expect students should take away from their reading courses.In another vein, and especially given the paucity of comparative evidence, it is extremelyinteresting to compare the intended reading and mathematics curriculum of more- and less-developed countries. To what extent, and in which areas, are there discernable differences in theintended mathematics and reading curriculum between these two groups of countries? In whatways do the general or specific findings emerging from this study compare to those found in theanalysis of more-developed countries? This is a fairly elaborate and challenging task, but severalinitial results can be noted. For example, the 2-dimensional geometry topics that appear in the setof the most prevalent mathematical contents in grades 5 and 6 represent a difference from what a1997 TIMSS study had found (Schmidt et al. 1997). In the earlier study 2-dimensional geometrytopics were mostly incorporated in the curricular content at or before grade 4, whereas 3-dimensional topics where rarely present in the intended curriculum--cross nationally--until aboutgrade 7 or 8. Some performance expectations such as ‗investigating and problem solving‘ werecommonly present in grade 4 TIMSS countries whereas they show up as ‗common‘ in Grade 6intended curricula in the present study. Such comparisons help to determine at which gradelevels specific knowledge domains in mathematics (or in reading) are incorporated in thecurriculum. In this study, for example, most of the developing countries have established a morechallenging set of mathematics performance expectations in grade 6 than in grade 5. In the futureit would be helpful to discern whether this trend is also apparent if grade 4 materials areanalyzed; and whether certain groups of countries--for example, defined by level ofdevelopment, region, or language—tend to establish a more ‗rigorous‘ curriculum than others.Another pertinent (and related) question, especially in light of previous discussions among IWGmembers, is: What implications can be drawn from the present study for assessing learningoutcomes in reading and mathematics in developing countries? Some preliminary ideas abouttesting are advanced here.In the area of mathematics, developing countries vary in the extent to which they require theinculcation of relatively complex mathematical skills. Given the variability of cognitively morechallenging performance expectations, it can be argued that their may be little demand for thedevelopment of capabilities in fielding complex performance assessments or other moreexpensive forms of standardized testing.The large number of content domains prevalent in the upper grade mathematics curriculum ofmany developing countries suggests that the most common types of testing schemes--namely,tests with small numbers of items (Carson 2009; Chakwera, Khembo, and Sireci 2004; Ravela etal. 2001; Valverde 1998, 2002, 2003, 2005, 2009)--are probably inappropriate for makinginferences regarding the achievement levels that students in a national educational system obtainin these varied curriculum areas. Learning assessments should be able to tell differenteducational stakeholders what school children are able (and not able) to do in specific 33
    • mathematical areas if in fact they are intended to serve as a basis for an informed, evidence-based dialogue regarding educational policy. An optimal number of items, providing sufficientgrounds for inferences about student achievement levels, is thought to be about 8 to 15. Primaryschool students in grades 5 and 6 can at best be asked to answer about 35 to 45 questions, whichare balanced in terms of cognitively complexity, without running up against a substantialproblem of omitted and/or not reached items. Thus, in order to field enough items to adequatelymeasure different domains would require a matrix sampling procedure with rotated test forms—ademanding and uncommon practice in the domestic testing systems of most developing countries(see above cited authors).Participation in international assessments, such as TIMSS, could be reconsidered. With the kindof detailed curricular information this project has produced, many developing countries couldpotentially benefit from participation in large-scale international studies. The key is making sureto complement the typical cross-national analyses with studies specifically focused on the testsubscales that are most aligned with their own national curricular contents and expectations.Indeed, when considering whether to participate in international testing programs, it is extremelyimportant for developing countries to develop the capacity to conduct sensible studies focusingon the curricular elements most aligned with their own curricular policies. This is not todisregard the importance of learning from other countries about students‘ abilities to masterspecific contents and skills in mathematics or reading, which are not included in the currentnational curriculum. For example, in the early 1990s the most optimistic estimates of thepercentage of school children taking Algebra in US middle schools was about 20% (Peak et al.1996). However, evidence of the good levels of achievements in algebra of the majority ofschool children in many TIMSS participating countries, led to substantial changes inmathematics expectations for US middle school students such that the majority take algebra.Thus, participation in these studies also provides an important opportunity to challenge localnotions of appropriate curricular expectations.In the area of reading, the implications for learning assessments are far more complex. As wehave seen, few developing countries currently share a vision of which type of written texts aremore or less important to utilize in the upper grades of primary education. It would be difficult toconstruct valid and feasible test instruments to assess different performance standards in readingcomprehension—around which there is considerable agreement—using different types (orcategories) of written texts.Future analysis will need to examine whether commonalities in types of text are more prevalentin the earlier primary grades (e.g., grade 4), in particular languages, or groups of countries. Thereading curriculum is intended to engender critical literacy skills among students, which havebeen shown to influence achievement in other areas of the school curriculum. With theseconcerns in mind, there is much value in expanding and enlarging the archive of curricularmaterials in reading, which this project has initiated. More in-depth analyses of the contents ofprimary school reading textbooks and official guidelines would help clarify how best, and inwhich specific knowledge domains, to assess reading-related learning outcomes among schoolchildren in developing countries. 34
    • VIII. Suggestions for future activitiesThrough the assistance of many individuals and agencies, this project has obtained, compiled andcoded curricular materials in reading and mathematics for a wide array of developing countriesin the world. The newly established international curriculum archive, known as ICATA, at theUniversity at Albany-SUNY fills a yawning gap in the existing knowledge base and should be ofinterest to many educational stakeholders. It also represents an important new resource to addresstimely and topical policy and scholarly issues concerning the primary school curriculum and,eventually, learning outcomes in the developing world.The current international archive can potentially be improved in the future by: Completing the coding of the existing compilation of curriculum documents, emergent findings could be validated and new lines of analysis can be pursued; and Selectively obtaining curriculum materials for certain countries, so as to complete the curricular files of cases examined in this study.The existing archive should be expanded to include: Mathematics and reading materials in the upper grades of primary education for countries in three ‗under-represented‘ regions: francophone Africa, Central Asia and certain Arab states (e.g., Egypt, Morocco, Sudan and in the Gulf). Curricular materials in the lower primary grades, especially in the area of reading, during which acquiring proficiency in an official language represents a basic building block for academic achievement in other subject areas. Curricular materials to the lower secondary grades (grades 7-9) to provide a more comprehensive picture of the knowledge base educational systems seek to provide during the basic education cycle. The intended curricular policies and textbooks in the areas of science and technology in the upper grades of primary education to identify commonalities and differences.The existing archive can be made more policy relevant by addressing language-related questions: To what extent does the language of instruction overlap with the language in which textbooks are provided? Which multi-lingual developing countries are presently providing textbooks in multiple languages, especially those spoken by members of indigenous groups as well as ethnic and linguistic minorities? Does the provision of language-specific curricular materials reduce repetition and increase completion rates in primary education? 35
    • For languages used in multiple education systems—for example, Arabic, Chinese, Spanish and English—are there clear associations between the specific contents and performance expectations of reading and mathematics and particular learning outcomes? In relation to the alignment issue: in which countries are intended curricular guidelines and textbook contents more or less closely aligned? What factors and policies appear to facilitate tighter alignment between the contents of official guidelines and textbooks?In sum, additional collaborative efforts—institutional, financial and analytical—are needed inorder to supplement the lessons learned from this study and add a new dynamic in on-goinginternational efforts to improve the quality of learning for all primary school age children. 36
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    • Pedagogical Flow: An Investigation of Mathematics and Science Teaching in Six Countries. Dordrecht, The Netherlands: Kluwer Academic Publishers.Schmidt, William H., Curtis C. McKnight, Gilbert A. Valverde, Richard T. Houang and David E. Wiley. 1997. Many Visions, Many Aims: A Cross-National Investigation of Curricular Intentions in School Mathematics. Vol. 1. Dordrecht, The Netherlands: Kluwer Academic Publishers.Simon, Martin A. 2006. Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals. Mathematical Thinking & Learning: An International Journal 8 (4):359-371Survey of Mathematics and Science Opportunities. 1992a. Document Analysis Manual. East Lansing, MI: SMSO.———. 1992b. Training Manual: Document Analysis, In-Depth Topic Trace Mapping Regional Training Meetings. East Lansing, MI: SMSO.———. 1993a. TIMSS Curriculum Analysis: A Content Analytic Approach. East Lansing, MI: SMSO.———. 1993b. TIMSS: Concepts, Measurements, and Analyses. East Lansing, MI: SMSO.University, Michigan State. 2006. Making the Grade: Fractions in Your Schools. Promoting Rigorous Outcomes in Mathematics and Science Education 1:8Torney-Purta, J., Lehmann, R., Oswald, H., & Schulz, W. 2001. Citizenship and education in twenty- eight countries: Civic knowledge and engagement at age fourteen. Delft, Netherlands: IEAUNESCO. 2000. The Dakar Framework for Action: Education for All - Meeting our Collective Commitments. World Education Forum, Dakar, UNESCO.———. 2007a. Enhancing Learning: From Access to Success. Report of the First Experts Meeting: Defining Areas of Action. Paris: 26 to 28 March, 2007. Paris: UNESCO.———. 2007b. Education for All by 2015: Will We Make It? Oxford: Oxford University Press and Paris: UNESCO.———. 2008. Overcoming Inequality: Why Governance Matters. Oxford: Oxford University Press and Paris: UNESCO.———. 2009. Reaching the Marginalized. Oxford: Oxford University Press and Paris: UNESCO.UNESCO Institute for Statistics (UIS). 2008. Global Education Digest 2008: Comparing education statistics across the world. Montreal: UIS.UNESCO-OREALC. 2007. The State of Education in Latin America and the Caribbean: Guaranteeing Quality Education for All. A Regional Report, Reviewing and Assessing the Progress of Latin America and the Caribbean toward Education for All within the Framework of the Regional Education Project (EFA/PRELAC). Santiago, UNESCO Regional Bureau for Education in Latin America and the CaribbeanValverde, Gilbert A. 1998. Evaluation and Curriculum Standards in an Era of Educational Reforms. In Evaluation and Education Reform: Policy Options, edited by B. Álvarez and M. Ruiz-Casares. Washington DC: U.S. Agency for International Development.———. 2000. Strategic Themes in Curriculum Policy Documents: An Exploration of TIMSS Curriculum Analysis Data. International Journal of Educational Policy Research and Practice. 1 (2):133-152.———. 2002. Curriculum: International. In The Encyclopedia of Education, edited by J. W. Guthrie. New York: Macmillan Reference.———. 2003. La Política en Evaluación y Currículo Ante el Desafío de la Calidad. In La Experiencia Internacional en Sistemas De Medición: Estudio De Casos, edited by Comisión para el Desarrollo y Uso del Sistema de Medición de la Calidad de la Educación. Santiago, Chile: SIMCE.———. 2003. Monitoring and evaluation of educational opportunities and learning in USAID sponsored projects in the Dominican Republic - technical proposal in response to RFP: 517-03-017 and amendment 1, of 09.03.2003. Albany, New York.———. 2005. Curriculum Policy Seen Through High-Stakes Examinations: Mathematics and Biology in a Selection of School-Leaving Examinations From the Middle East and North Africa. Peabody Journal of Education 80 (1):29-55. 39
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    • Important Note to Tables 2 through 9Tables 2-9 are organized to highlight the ―common‖ contents and performance expectationsfound in a range of textbooks or curricular statements in mathematics and reading at differentgrade levels. The term ―common‖ is used in a very particular way in these tables. It refers to thefact that those elements listed under Content and Performance Expectations (of all the possibleelements that were possible to identify in a country‘s textbook or curricular statement) were heldin common in 70% of the countries listed. So, for example, Table 2 lists those elements inmathematics, which were found in at least 23 of the 33 national grade 6 textbooks analyzed.Other mathematics topics and performance standards, which are NOT listed, fell below the 70%benchmark and thus are not held in ―common.‖Table 2: Common contents and performance expectations in grade 6, based on an analysis of textbooks in mathematicsNumber of countries in the analysis= 33List of countries: Afghanistan, Argentina, Brazil, Cambodia, Chile, China, Colombia, CostaRica, Dominican Republic, Egypt, Hong Kong, India, Iran, Indonesia, Jordan, Lebanon, Mexico,Pakistan, Palestinian National Authority, Paraguay, Peru, Philippines, Senegal, Shanghai(China), Sri Lanka, Sudan (southern), Taiwan, Thailand, Uganda, United Arab Emirates,Uzbekistan, Venezuela, Vietnam.1 Mathematics Content11 1.1 Numbers## 1.1.1 Whole Numbers## 1.1.1.1 Meaning## The uses of numbers## Place value & numeration## Ordering & comparing numbers## 1.1.1.2 Operations## Addition## Subtraction## Multiplication## Division Mixed Operations#### 1.1.2 Fractions & Decimals## 1.1.2.1 Common Fractions## Meaning & representation of common fractions## Computations with common fractions & mixed numbers## 1.1.2.2 Decimal Fractions## Meaning & representation of decimals## Computations with decimals## 1.1.2.3. Relationships of Common & Decimal Fractions## Conversion to equivalent forms## Ordering of fractions & decimals 41
    • ## 1.1.2.4 Percentages## Percent computations Various types of percent problems##12 1.2 Measurement## 1.2.1 Measurement Units## Concept of measure (including non-standard units)## Standard units (including metric system)## Use of appropriate instruments## Common measures ( Length; area; volume; time; calendar; money; temp; mass; weight; angles)## Quotients and products of units (km/h, m/s, etc.)## Dimensional analysis## 1.2.2 Computations & Properties of Length, Perimeter, Area & Volume## Computations, formulas and properties of length and perimeter## Computations, formulas and properties of area## Computations, formulas and properties of surface area Computations, formulas and properties of volumes##13 1.3 Geometry: Position, Visualization & Shape## 1.3.2 2-D Geometry: Basics## Points, lines, segments, half-lines, and rays## Angles## Parallelism and perpendicularity## 1.3.3 2-D Geometry: Polygons & Circles## Triangles and quadrilaterals: their classification and properties## Pythagorean Theorem and its applications## Other polygons and their properties## Circles and their properties## 1.3.4 3-D Geometry## 3-Dimensional shapes and surfaces and their properties## Planes and lines in space## Spatial perception and visualization## Coordinate systems in three dimensions## Equations of lines, planes and surfaces in space15 1.5 Proportionality## 1.5.1 Proportionality Concepts## Meaning of ratio and proportion## Direct and inverse proportion17 1.7 Data Representation, Probability, & Statistics## 1.7.1 Data Representation & Analysis## Collecting data from experiments and simple surveys## Representing data## Interpreting tables, charts, plots, graphs## Kinds of scales (nominal, ordinal, interval, ratio)## Measures of central tendency## Measures of dispersion## Sampling, randomness, and bias related to data samples## Prediction and inferences from data 42
    • ## Fitting lines and curves to data## Correlations and other measures of relations## Use and misuse of statistics2 Performance Expectations 2.1 Knowing 2.1.1 Representing Select an appropriate representation Construct an appropriate informal representation for the subject (e.g., a sketch) Construct a formal representation governed by strict construction procedures (e.g., geometric construction) 2.1.2 Recognizing equivalents Indicate recognition of an equivalence by identification or selection Construct an object equivalent to a given object or two equivalent object of a certain category Select or construct an object and its equivalent decomposition or two equivalent decompositions (e.g., prime factorizations of whole numbers, matrix products, etc.) 2.1.3 Recalling mathematical objects and properties Recalling mathematical objects and properties Recognizing mathematical objects and properties 2.2 Using routine procedures 2.2.1 Using equipment 2.2.1.1 Using instruments, for example, measuring instruments 2.2.2 Performing routine procedures 2.2.2.2 Computing Identify an appropriate single computational operation Identify an appropriate single computational method Predict the effect of a computation operation or method Perform a single computational operation (e.g., multiply decimal fractions or matrices) Compute without aid of a computational device using an ad hoc procedure Compute without aid of a computational device using a known algorithm or procedure Compute by use of a formula (e.g., compute a mean) Compute using results of a simulation (e.g., find a probability on the basis of simulated experiment) Compute using inference and properties of a model (e.g., find a probability using a simple probability model) 2.2.2.5 Measuring Measure of a physical object, iconic (pictorial) image or geometric figure in either standard or non-standard units Identify a measurable attribute of a physical object or image Select an appropriate unit for a given measurement Select an appropriate tool for a given measurement Select an appropriate degree of accuracy for a measurement in a given situation and task 2.3 Investigating and problem solving 43
    • 2.3.3 Solving Solve a problem requiring a single step or operation Solve a problem requiring more than one step or operation Solve by transforming a representation (e.g., solve equations by algebraic manipulations to yield a sequence of equivalent equations) Solve the same problem in alternative ways using differing representations 44
    • Table 3: Common contents and performance expectations in grades 5 and 6, based on an analysis of textbooks in mathematicsNumber of countries in the analysis= 31List of countries: Argentina, Brazil, Cambodia, Chile, China, Colombia, Costa Rica, DominicanRepublic, Egypt, Hong Kong, India, Iran, Indonesia, Jordan, Lebanon, Mexico, Pakistan,Palestinian National Authority, Paraguay, Peru, Philippines , Senegal, Shanghai, Sri Lanka,Taiwan, Thailand, Uganda, United Arab Emirates, Uzbekistan, Venezuela, Vietnam.1 Mathematics Content11 1.1 Numbers## 1.1.1 Whole Numbers## 1.1.1.1 Meaning## The uses of numbers## Place value & numeration## Ordering & comparing numbers## 1.1.1.2 Operations## Addition## Subtraction## Multiplication## Division## Mixed Operations## 1.1.1.3 Properties of Operations## Associative properties## Commutative properties## Identity properties## Distributive properties## Other number properties## 1.1.2 Fractions & Decimals## 1.1.2.1 Common Fractions## Meaning & representation of common fractions## Computations with common fractions & mixed numbers## 1.1.2.2 Decimal Fractions## Meaning & representation of decimals## Computations with decimals## 1.1.2.3. Relationships of Common & Decimal Fractions## Conversion to equivalent forms## Ordering of fractions & decimals## 1.1.2.4 Percentages## Percent computations## Various types of percent problems## 1.1.2.5 Properties of Common & Decimal Fractions## Associative properties## Commutative properties## Identity properties## Inverse properties## Distributive properties 45
    • ## Cancellation properties## Other number properties## 1.1.4 Other Numbers & Number Concepts## 1.1.4.4 Number Theory## Primes & Factorization## Elementary number theory, etc.12 1.2 Measurement## 1.2.1 Measurement Units## Concept of measure (including non-standard units)## Standard units (including metric system)## Use of appropriate instruments## Common measures ( Length; area; volume; time; calendar; money; temp; mass; weight; angles)## Quotients and products of units (km/h, m/s, etc.)## Dimensional analysis## 1.2.2 Computations & Properties of Length, Perimeter, Area & Volume## Computations, formulas and properties of length and perimeter## Computations, formulas and properties of area## Computations, formulas and properties of surface area## Computations, formulas and properties of volumes13 1.3 Geometry: Position, Visualization & Shape## 1.3.1 1-D & 2-D Coordinate Geometry## Line and coordinate graphs## Equations of lines in a plane## Conic sections and their equations## 1.3.2 2-D Geometry: Basics## Points, lines, segments, half-lines, and rays## Angles## Parallelism and perpendicularity## 1.3.3 2-D Geometry: Polygons & Circles## Triangles and quadrilaterals: their classification and properties## Pythagorean Theorem and its applications## Other polygons and their properties## Circles and their properties## 1.3.4 3-D Geometry## 3-Dimensional shapes and surfaces and their properties## Planes and lines in space## Spatial perception and visualization## Coordinate systems in three dimensions## Equations of lines, planes and surfaces in space15 1.5 Proportionality## 1.5.1 Proportionality Concepts## Meaning of ratio and proportion## Direct and inverse proportion## 1.5.2 Proportionality Problems## Solving proportional equations## Solving practical problems with proportionality## Scales (maps and plans)## Proportion based on similarity 1.7 Data Representation, Probability, & Statistics 46
    • 17## 1.7.1 Data Representation & Analysis## Collecting data from experiments and simple surveys## Representing data## Interpreting tables, charts, plots, graphs## Kinds of scales (nominal, ordinal, interval, ratio)## Measures of central tendency## Measures of dispersion## Sampling, randomness, and bias related to data samples## Prediction and inferences from data## Fitting lines and curves to data## Correlations and other measures of relations## Use and misuse of statistics2 Performance Expectations 2.1 Knowing 2.1.1 Representing Select an appropriate representation Construct an appropriate informal representation for the subject (e.g., a sketch) Construct a formal representation governed by strict construction procedures (e.g., geometric construction) 2.1.2 Recognizing equivalents Indicate recognition of an equivalence by identification or selection Construct an object equivalent to a given object or two equivalent object of a certain category Select or construct an object and its equivalent decomposition or two equivalent decompositions (e.g., prime factorizations of whole numbers, matrix products, etc.) 2.1.3 Recalling mathematical objects and properties Recalling mathematical objects and properties Recognizing mathematical objects and properties 2.2 Using routine procedures 2.2.1 Using equipment 2.2.1.1 Using instruments, for example, measuring instruments 2.2.2 Performing routine procedures 2.2.2.1 Counting 2.2.2.2 Computing Identify an appropriate single computational operation Identify an appropriate single computational method Predict the effect of a computation operation or method Perform a single computational operation (e.g., multiply decimal fractions or matrices) Compute without aid of a computational device using an ad hoc procedure Compute without aid of a computational device using a known algorithm or procedure Compute by use of a formula (e.g., compute a mean) Compute using results of a simulation (e.g., find a probability on the basis of simulated experiment) Compute using inference and properties of a model (e.g., find a probability using a simple probability model) 2.2.2.3 Graphing Construct a coordinate graph by performing computations if necessary and plotting one or more points. Multiple points may be left unconnected, connected 47
    • with line segments in a line graph, or connected by a smooth curve approximating that which would be obtained by extrapolating between points Construct a coordinate graph by use of known properties of the object being graphed (usually assigning of at least one point specifically, for example, a y-intercept) Construct a coordinate graph by use of a graphing calculator or microcomputer (no manual point assignment) 2.2.2.5 Measuring Measure of a physical object, iconic (pictorial) image or geometric figure in either standard or non-standard units Identify a measurable attribute of a physical object or image Select an appropriate unit for a given measurement Select an appropriate tool for a given measurement Select an appropriate degree of accuracy for a measurement in a given situation and task 2.2.3 Using more complex procedures 2.2.3.1 Estimating Decide when an estimate rather than an exact answer is appropriate Estimate a single quantity (e.g., a count) Estimate a ratio (e.g., of shaded area to total area in a geometric figure) Estimate a measurement (possibly including partitioning the figure) Estimate a result of a computational operation or procedure Decide if the result of an exact computation is reasonable by performing mentally or explicitly an approximate computation Identify the range of a "good estimate" Round a quantity using an algorithm or representation (e.g., a number line) Select a number closest in size to a number of another type (e.g., fraction to whole number) Approximate by an algorithmic or iterative procedure (e.g., approximate a zero of a polynomial by iteration) 2.2.3.2 Using data Collect data by surveys, samples, measurement, etc. Organize data by tallies, categorization, etc. Construct a data display (e.g., non-coordinate graph, frequency distribution, etc.) Read, interpret a data display and/or use it to answer a question Choose an appropriate data display for a given communication or problem-solving situation Fit a curve of a given type to a set of data 2.2.3.4 Classifying Recognize examples and non-examples of a class of objects (e.g., proportions) Classify mathematics objects by implicit criteria (e.g., geometric shapes) Classify mathematics objects by explicit criteria Identify properties defining a class (e.g., shapes; symmetries; similarities or congruencies by behavior under specified transformations, etc.) Select or state the formal defining properties of a class2.3 Investigating and problem solving 2.3.1 Formulating and clarifying problems and situations Construct a verbal or symbolic statement of a real-world or other situation in which a mathematical problem goal can be specified Simplify a real-world or other problem situation by selecting aspects and relationships to be captured in a representation modeling the situation Select or construct a mathematical representation of a real-world situation or other problem situation 48
    • Select or construct a mathematical representation of a problem (real-world or other problem situation plus a related question/goal) Compare and contrast two real world situations with quantitative aspects (e.g., by using measurements of each or quantities associated with each) Describe the effect of a change in a situation (e.g., the effect on its graph of changing a parameter) Determine data or the range of data needed to solve a data-related problem2.3.3 Solving Solve a problem requiring a single step or operation Solve a problem requiring more than one step or operation Solve by transforming a representation (e.g., solve equations by algebraic manipulations to yield a sequence of equivalent equations) Solve the same problem in alternative ways using differing representations 49
    • Table 4: Common contents and performance expectations in grades 6, based on an analysis of curriculum statements and guidelines in mathematicsNumber of countries in the analysis= 27List of countries: Argentina, Bahamas, Belize, Bermuda, Botswana, Cambodia, Chile, China,Colombia, Costa Rica, Dominican Republic, El Salvador, Guatemala, Jamaica, Lesotho, Namibia,Nicaragua, Pakistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines , St. Lucia, SriLanka, Taiwan, Thailand.1 Mathematics Content11 1.1 Numbers## 1.1.1 Whole Numbers## 1.1.1.1 Meaning## The uses of numbers## Place value & numeration## Ordering & comparing numbers## 1.1.1.2 Operations## Addition## Subtraction## Multiplication## Division Mixed Operations#### 1.1.2 Fractions & Decimals## 1.1.2.1 Common Fractions## Meaning & representation of common fractions## Computations with common fractions & mixed numbers## 1.1.2.2 Decimal Fractions## Meaning & representation of decimals## Computations with decimals## 1.1.2.4 Percentages## Percent computations Various types of percent problems##12 1.2 Measurement## 1.2.1 Measurement Units## Concept of measure (including non-standard units)## Standard units (including metric system)## Use of appropriate instruments## Common measures ( Length; area; volume; time; calendar; money; temp; mass; weight; angles)## Quotients and products of units (km/h, m/s, etc.)## Dimensional analysis## 1.2.2 Computations & Properties of Length, Perimeter, Area & Volume## Computations, formulas and properties of length and perimeter## Computations, formulas and properties of area## Computations, formulas and properties of surface area 50
    • ## Computations, formulas and properties of volumes13 1.3 Geometry: Position, Visualization & Shape## 1.3.2 2-D Geometry: Basics## Points, lines, segments, half-lines, and rays## Angles## Parallelism and perpendicularity## 1.3.3 2-D Geometry: Polygons & Circles## Triangles and quadrilaterals: their classification and properties## Pythagorean Theorem and its applications## Other polygons and their properties## Circles and their properties## 1.3.4 3-D Geometry## 3-Dimensional shapes and surfaces and their properties## Planes and lines in space## Spatial perception and visualization## Coordinate systems in three dimensions## Equations of lines, planes and surfaces in space17 1.7 Data Representation, Probability, & Statistics## 1.7.1 Data Representation & Analysis## Collecting data from experiments and simple surveys## Representing data## Interpreting tables, charts, plots, graphs## Kinds of scales (nominal, ordinal, interval, ratio)## Measures of central tendency## Measures of dispersion## Sampling, randomness, and bias related to data samples## Prediction and inferences from data## Fitting lines and curves to data## Correlations and other measures of relations## Use and misuse of statistics2 Performance Expectations 2.1 Knowing 2.1.1 Representing Select an appropriate representation Construct an appropriate informal representation for the subject (e.g., a sketch) Construct a formal representation governed by strict construction procedures (e.g., geometric construction) 2.1.3 Recalling mathematical objects and properties Recalling mathematical objects and properties Recognizing mathematical objects and properties 2.2 Using routine procedures 2.2.2 Performing routine procedures 2.2.2.2 Computing Identify an appropriate single computational operation Identify an appropriate single computational method Predict the effect of a computation operation or method 51
    • Perform a single computational operation (e.g., multiply decimal fractions or matrices) Compute without aid of a computational device using an ad hoc procedure Compute without aid of a computational device using a known algorithm or procedure Compute by use of a formula (e.g., compute a mean) Compute using results of a simulation (e.g., find a probability on the basis of simulated experiment) Compute using inference and properties of a model (e.g., find a probability using a simple probability model) 2.2.2.5 Measuring Measure of a physical object, iconic (pictorial) image or geometric figure in either standard or non-standard units Identify a measurable attribute of a physical object or image Select an appropriate unit for a given measurement Select an appropriate tool for a given measurement Select an appropriate degree of accuracy for a measurement in a given situation and task2.3 Investigating and problem solving 2.3.3 Solving Solve a problem requiring a single step or operation Solve a problem requiring more than one step or operation Solve by transforming a representation (e.g., solve equations by algebraic manipulations to yield a sequence of equivalent equations) Solve the same problem in alternative ways using differing representations 52
    • Table 5: Common contents and performance expectations in grades 5 and 6,based on an analysis of curriculum statements and guidelines in mathematicsNumber of countries in the analysis= 30List of countries: Argentina, Bahamas, Belize, Bermuda, Botswana, Cambodia, Chile, China,Colombia, Costa Rica, Dominican Republic, El Salvador, Guatemala, Hong Kong, Jamaica,Lesotho, Mauritius, Mexico, Namibia, Nicaragua, Pakistan, Panama, Paraguay, Peru,Philippines, St. Lucia, South Africa, Sri Lanka, Thailand, Taiwan.1 Mathematics Content11 1.1 Numbers## 1.1.1 Whole Numbers## 1.1.1.1 Meaning## The uses of numbers## Place value & numeration## Ordering & comparing numbers## 1.1.1.2 Operations## Addition## Subtraction## Multiplication## Division## Mixed Operations## 1.1.1.3 Properties of Operations## Associative properties## Commutative properties## Identity properties## Distributive properties## Other number properties## 1.1.2 Fractions & Decimals## 1.1.2.1 Common Fractions## Meaning & representation of common fractions## Computations with common fractions & mixed numbers## 1.1.2.2 Decimal Fractions## Meaning & representation of decimals Computations with decimals##12 1.2 Measurement## 1.2.1 Measurement Units## Concept of measure (including non-standard units)## Standard units (including metric system)## Use of appropriate instruments## Common measures ( Length; area; volume; time; calendar; money; temp; mass; weight; angles)## Quotients and products of units (km/h, m/s, etc.)## Dimensional analysis## 1.2.2 Computations & Properties of Length, Perimeter, Area & Volume 53
    • ## Computations, formulas and properties of length and perimeter## Computations, formulas and properties of area## Computations, formulas and properties of surface area## Computations, formulas and properties of volumes13 1.3 Geometry: Position, Visualization & Shape## 1.3.2 2-D Geometry: Basics## Points, lines, segments, half-lines, and rays## Angles## Parallelism and perpendicularity## 1.3.3 2-D Geometry: Polygons & Circles## Triangles and quadrilaterals: their classification and properties## Pythagorean Theorem and its applications## Other polygons and their properties## Circles and their properties## 1.3.4 3-D Geometry## 3-Dimensional shapes and surfaces and their properties## Planes and lines in space## Spatial perception and visualization## Coordinate systems in three dimensions Equations of lines, planes and surfaces in space##17 1.7 Data Representation, Probability, & Statistics## 1.7.1 Data Representation & Analysis## Collecting data from experiments and simple surveys## Representing data## Interpreting tables, charts, plots, graphs## Kinds of scales (nominal, ordinal, interval, ratio)## Measures of central tendency## Measures of dispersion## Sampling, randomness, and bias related to data samples## Prediction and inferences from data## Fitting lines and curves to data## Correlations and other measures of relations## Use and misuse of statistics2 Performance Expectations 2.1 Knowing 2.1.1 Representing Select an appropriate representation Construct an appropriate informal representation for the subject (e.g., a sketch) Construct a formal representation governed by strict construction procedures (e.g., geometric construction) 2.1.2 Recognizing equivalents Indicate recognition of an equivalence by identification or selection Construct an object equivalent to a given object or two equivalent object of a certain category Select or construct an object and its equivalent decomposition or two equivalent decompositions (e.g., prime factorizations of whole numbers, matrix products, etc.) 2.1.3 Recalling mathematical objects and properties Recalling mathematical objects and properties Recognizing mathematical objects and properties 54
    • 2.2 Using routine procedures 2.2.2 Performing routine procedures 2.2.2.1 Counting 2.2.2.2 Computing Identify an appropriate single computational operation Identify an appropriate single computational method Predict the effect of a computation operation or method Perform a single computational operation (e.g., multiply decimal fractions or matrices) Compute without aid of a computational device using an ad hoc procedure Compute without aid of a computational device using a known algorithm or procedure Compute by use of a formula (e.g., compute a mean) Compute using results of a simulation (e.g., find a probability on the basis of simulated experiment) Compute using inference and properties of a model (e.g., find a probability using a simple probability model) 2.2.2.5 Measuring Measure of a physical object, iconic (pictorial) image or geometric figure in either standard or non-standard units Identify a measurable attribute of a physical object or image Select an appropriate unit for a given measurement Select an appropriate tool for a given measurement Select an appropriate degree of accuracy for a measurement in a given situation and task 2.2.3 Using more complex procedures 2.2.3.2 Using data Collect data by surveys, samples, measurement, etc. Organize data by tallies, categorization, etc. Construct a data display (e.g., non-coordinate graph, frequency distribution, etc.) Read, interpret a data display and/or use it to answer a question Choose an appropriate data display for a given communication or problem-solving situation Fit a curve of a given type to a set of data2.3 Investigating and problem solving 2.3.3 Solving Solve a problem requiring a single step or operation Solve a problem requiring more than one step or operation Solve by transforming a representation (e.g., solve equations by algebraic manipulations to yield a sequence of equivalent equations) Solve the same problem in alternative ways using differing representations 55
    • Table 6: Common contents and performance expectations in grade 6, based on an analysis of textbooks in readingNumber of countries in the analysis= 32List of countries: Argentina, Bahamas, Brazil, Cambodia, China, Colombia, Costa Rica,Dominican Republic, Egypt, Ghana, Hong Kong, India, Indonesia, Jordan, Lebanon , Libya,Mexico, Pakistan, Palestinian National Authority, Paraguay, Peru, Philippines, Shanghai, St.Lucia, Syria, Thailand, Taiwan, Uganda, United Arab Emirates, Uzbekistan, Venezuela,Vietnam.1. Content 1.1 Types of written texts 1.1.13 Story / Tale 1.1.54 Poem 1.2 Acts of Speech 1.2.18 Dialogue 1.3 Function 1.3.1 Informative 1.4 Types of Plot 1.4.2 Narrative 1.4.3 Descriptive2. Performance expectations (skills/competences to be acquired) 2.1 Literal comprehension (elements explicitly found in the text) 2.1.1 Explicit information found in the text Identify Extract Find Remember 2.2 Inferential comprehension (use/handling of implicit elements in the text). 2.2.1 Types of inference, according to the operation Differentiate Compare Deduct Generalize Apply Interpret Reorganize Relate/Connect Summarize Paraphrase Include 56
    • Table 7: Common contents and performance expectations in grades 5&6 , based on an analysis of textbook in readingNumber of countries in the analysis= 29List of countries: Argentina, Bahamas, Brazil, Cambodia, China, Colombia, Costa Rica,Dominican Republic, Egypt, Ghana, Hong Kong, India, Indonesia, Jordan, Lebanon, Libya,Mexico, Pakistan, Palestinian National Authority, Paraguay, St. Lucia, Syria, Thailand, Taiwan,Uganda, United Arab Emirates, Uzbekistan, Venezuela, Vietnam.1. Content 1.1. Types of written texts 1.1.6 Biography 1.1.7 Letter 1.1.13 Story/Tale 1.1.52 Play 1.1.54 Poem 1.1.61 Historic account 1.2 Acts of Speech 1.2.18 Dialogue 1.3 Function 1.3.1 Informative 1.4 Types of Plot 1.4.1 Narrative 1.4.2 Descriptive 1.4.3 Explanatory, expositive 1.6. Structural Elements of the Plot 1.6.1 Categories and types of relations Cause Effect Problem Solution Event (occurrence) Opinion Information, facts (statistical, nutritional) Anecdote Explanation Details (Characteristics) Message (moral) Object 57
    • Ingredient Preparation Motivation (motive, issue, interest) Environment (context, atmosphere, time, place) Action Order (lineal, half of the story, at the end) Type 1.6.2 Narrative point of view In first person In second person In third person 1.12. Reading mode Out loud In silence Scanning and Skimming2. Performance expectations (skills/competences to be acquired) 2.1. Literal comprehension (elements explicitly found in the text) 2.1.1.Explicit information found in the text Identify Extract Find Remember 2.2. Inferential comprehension (use/handling of implicit elements in the text). 2.2.1.Types of inference, according to the operation Differentiate Compare Deduct Generalize Apply Interpret Reorganize Relate/Connect Summarize Paraphrase Include 2.4 . Metacomprehension 2.4.4 Generate mental images 58
    • Table 8: Common contents and performance expectations in grades 6, based on an analysis of curriculum statements and guidelines in readingNumber of countries in the analysis= 23List of countries: Bahamas, Bermuda, Botswana, Cambodia, Caribbean, Chile, Colombia, CostaRica, Dominican Republic, El Salvador, Guatemala, Jamaica, Lesotho, Mexico, Nicaragua,Pakistan, Panama, Paraguay, Peru, Philippines, South Africa, Sri Lanka, Thailand.2. Performance expectations (skills/competences to be acquired) 2.1. Literal comprehension (elements explicitly found in the text) 2.1.1. Explicit information found in the text Identify Extract Find Remember 2.2. Inferential comprehension (use/handling of implicit elements in the text). 2.2.1. Types of inference, according to the operation Differentiate Compare Deduct Generalize Apply Interpret Reorganize Relate/Connect Summarize Paraphrase Include 2.3. Value or evaluative comprehension (judge reading elements against values, norms, and criteria) 2.3.1. Judgments about Precision-vagueness Coherence-incoherence Complexity-simplicity Validity and/or reliability Completeness of the information The probability or plausibility The contrast with values and/or personal experience The contrast with socio-cultural values or experiences 59
    • Table 9: Common contents and performance expectations in grades 5 and 6, based on an analysis of curriculum statements and guidelines in readingNumber of countries in the analysis= 25List of countries: Bahamas, Bermuda, Botswana, Cambodia, Caribbean, Chile, Colombia, CostaRica, Dominican Republic, El Salvador, Guatemala, Hong Kong, Jamaica, Lesotho, Mauritius,Mexico, Nicaragua, Pakistan, Panama, Paraguay, Peru, Philippines, Sri Lanka, Thailand,Taiwan. 1. Content 1.1 Types of written texts 1.1.54 poem 1.3. Function 1.3.1. Informative2. Performance expectations (skills/competences to be acquired) 2.4. Literal comprehension (elements explicitly found in the text) 2.4.1. Explicit information found in the text Identify Extract Find Remember 2.5. Inferential comprehension (use/handling of implicit elements in the text). 2.5.1. Types of inference, according to the operation Differentiate Compare Deduct Generalize Apply Interpret Reorganize Relate/Connect Summarize Paraphrase Include 2.6. Value or evaluative comprehension (judge reading elements against values, norms, and criteria) 2.6.1. Judgments about Precision-vagueness 60
    • Coherence-incoherenceComplexity-simplicityValidity and/or reliabilityCompleteness of the informationThe probability or plausibilityThe contrast with values and/or personal experienceThe contrast with socio-cultural values or experiences 61